| $2$
| \( ( 1 + T )^{14} \)
|
| $3$
| \( \)
|
| $5$
| \( 1 + 2 T + 28 T^{2} + 60 T^{3} + 435 T^{4} + 932 T^{5} + 4641 T^{6} + 9874 T^{7} + 37720 T^{8} + 79480 T^{9} + 249270 T^{10} + 522542 T^{11} + 1421451 T^{12} + 2950348 T^{13} + 7372677 T^{14} + 14751740 T^{15} + 35536275 T^{16} + 65317750 T^{17} + 155793750 T^{18} + 248375000 T^{19} + 589375000 T^{20} + 771406250 T^{21} + 1812890625 T^{22} + 1820312500 T^{23} + 4248046875 T^{24} + 2929687500 T^{25} + 6835937500 T^{26} + 2441406250 T^{27} + 6103515625 T^{28} \)
|
| $7$
| \( 1 - 4 T + 41 T^{2} - 141 T^{3} + 886 T^{4} - 2702 T^{5} + 13194 T^{6} - 36749 T^{7} + 152933 T^{8} - 396432 T^{9} + 1481221 T^{10} - 3629234 T^{11} + 12465202 T^{12} - 28914434 T^{13} + 92675285 T^{14} - 202401038 T^{15} + 610794898 T^{16} - 1244827262 T^{17} + 3556411621 T^{18} - 6662832624 T^{19} + 17992414517 T^{20} - 30264381707 T^{21} + 76060784394 T^{22} - 109035446114 T^{23} + 250273070614 T^{24} - 278803070763 T^{25} + 567492775241 T^{26} - 387556041628 T^{27} + 678223072849 T^{28} \)
|
| $11$
| \( 1 + 2 T + 61 T^{2} + 136 T^{3} + 2029 T^{4} + 4541 T^{5} + 47979 T^{6} + 102861 T^{7} + 894464 T^{8} + 1797910 T^{9} + 13870329 T^{10} + 26073088 T^{11} + 184810378 T^{12} + 326416620 T^{13} + 2161407870 T^{14} + 3590582820 T^{15} + 22362055738 T^{16} + 34703280128 T^{17} + 203075486889 T^{18} + 289555203410 T^{19} + 1584597538304 T^{20} + 2004469896231 T^{21} + 10284724751499 T^{22} + 10707440464831 T^{23} + 52627034515429 T^{24} + 38802387203096 T^{25} + 191444130979981 T^{26} + 69045424287862 T^{27} + 379749833583241 T^{28} \)
|
| $13$
| \( 1 - 4 T + 55 T^{2} - 164 T^{3} + 1841 T^{4} - 5834 T^{5} + 51222 T^{6} - 152916 T^{7} + 1105419 T^{8} - 3168570 T^{9} + 20685432 T^{10} - 57342178 T^{11} + 333039468 T^{12} - 858558930 T^{13} + 4596254473 T^{14} - 11161266090 T^{15} + 56283670092 T^{16} - 125980765066 T^{17} + 590796623352 T^{18} - 1176467861010 T^{19} + 5335646377971 T^{20} - 9595252225572 T^{21} + 41783358991062 T^{22} - 61866649342082 T^{23} + 253797483494009 T^{24} - 293914304622068 T^{25} + 1281394681736455 T^{26} - 1211500426369012 T^{27} + 3937376385699289 T^{28} \)
|
| $17$
| \( 1 + 9 T + 116 T^{2} + 734 T^{3} + 5894 T^{4} + 33374 T^{5} + 217597 T^{6} + 1158998 T^{7} + 6467809 T^{8} + 31916274 T^{9} + 160080026 T^{10} + 734570171 T^{11} + 3403169256 T^{12} + 14440220552 T^{13} + 62194715466 T^{14} + 245483749384 T^{15} + 983515914984 T^{16} + 3608943250123 T^{17} + 13370043851546 T^{18} + 45316545052818 T^{19} + 156117186016321 T^{20} + 475581701329654 T^{21} + 1517903891889277 T^{22} + 3957751790210878 T^{23} + 11882268049246406 T^{24} + 25155571889802622 T^{25} + 67584179518652276 T^{26} + 89141202296153433 T^{27} + 168377826559400929 T^{28} \)
|
| $19$
| \( 1 - 14 T + 169 T^{2} - 1403 T^{3} + 11488 T^{4} - 78175 T^{5} + 522320 T^{6} - 3035681 T^{7} + 17497829 T^{8} - 90997285 T^{9} + 473230201 T^{10} - 2251728068 T^{11} + 10805853754 T^{12} - 48136741502 T^{13} + 217617850140 T^{14} - 914598088538 T^{15} + 3900913205194 T^{16} - 15444602818412 T^{17} + 61671833024521 T^{18} - 225318286391215 T^{19} + 823200780892349 T^{20} - 2713509454519259 T^{21} + 8870854647575120 T^{22} - 25226110773873325 T^{23} + 70433689169617888 T^{24} - 163435833234201257 T^{25} + 374050221322181209 T^{26} - 588741768471598826 T^{27} + 799006685782884121 T^{28} \)
|
| $23$
| \( 1 + 30 T + 584 T^{2} + 8287 T^{3} + 96925 T^{4} + 963908 T^{5} + 8497143 T^{6} + 67352281 T^{7} + 489924256 T^{8} + 3292775643 T^{9} + 20674520004 T^{10} + 121569332525 T^{11} + 673577436637 T^{12} + 3516529515759 T^{13} + 17358630554967 T^{14} + 80880178862457 T^{15} + 356322463980973 T^{16} + 1479134068831675 T^{17} + 5785578352439364 T^{18} + 21193433460393549 T^{19} + 72526372779623584 T^{20} + 229322760262294607 T^{21} + 665419640403552183 T^{22} + 1736145459605477404 T^{23} + 4015264599382929325 T^{24} + 7895934463832713049 T^{25} + 12798140668299867464 T^{26} + 15121090858094021490 T^{27} + 11592836324538749809 T^{28} \)
|
| $29$
| \( 1 + 6 T + 181 T^{2} + 1020 T^{3} + 14668 T^{4} + 73882 T^{5} + 710119 T^{6} + 2807471 T^{7} + 22480794 T^{8} + 45950648 T^{9} + 431717642 T^{10} - 836466161 T^{11} + 2151226620 T^{12} - 73261063515 T^{13} - 88428928137 T^{14} - 2124570841935 T^{15} + 1809181587420 T^{16} - 20400573200629 T^{17} + 305345685551402 T^{18} + 942500587774552 T^{19} + 13372100545796874 T^{20} + 48428527491104539 T^{21} + 355234482525452359 T^{22} + 1071816958989153458 T^{23} + 6170933698047348268 T^{24} + 12444519961019945580 T^{25} + 64040475760189896421 T^{26} + 61563772277751613134 T^{27} + \)\(29\!\cdots\!81\)\( T^{28} \)
|
| $31$
| \( 1 - 11 T + 293 T^{2} - 2401 T^{3} + 37974 T^{4} - 249434 T^{5} + 3040390 T^{6} - 16528313 T^{7} + 172961258 T^{8} - 792069810 T^{9} + 7626311273 T^{10} - 30088144642 T^{11} + 280194802802 T^{12} - 994265734303 T^{13} + 9112906214803 T^{14} - 30822237763393 T^{15} + 269267205492722 T^{16} - 896355917029822 T^{17} + 7043058613152233 T^{18} - 22676286193031310 T^{19} + 153503753145390698 T^{20} - 454737097474824743 T^{21} + 2593121381325241990 T^{22} - 6594940714024810214 T^{23} + 31124564569808937174 T^{24} - 61005753028267999231 T^{25} + \)\(23\!\cdots\!73\)\( T^{26} - \)\(26\!\cdots\!01\)\( T^{27} + \)\(75\!\cdots\!21\)\( T^{28} \)
|
| $37$
| \( 1 - 13 T + 281 T^{2} - 3111 T^{3} + 40264 T^{4} - 367589 T^{5} + 3638571 T^{6} - 28152253 T^{7} + 231032713 T^{8} - 1552251607 T^{9} + 11156663741 T^{10} - 67286788305 T^{11} + 447921138414 T^{12} - 2557243358182 T^{13} + 16700844235102 T^{14} - 94618004252734 T^{15} + 613204038488766 T^{16} - 3408277688013165 T^{17} + 20909384073496301 T^{18} - 107639268688988899 T^{19} + 592766733087017617 T^{20} - 2672546222813130649 T^{21} + 12780405879132786891 T^{22} - 47772505969532559353 T^{23} + \)\(19\!\cdots\!36\)\( T^{24} - \)\(55\!\cdots\!43\)\( T^{25} + \)\(18\!\cdots\!61\)\( T^{26} - \)\(31\!\cdots\!61\)\( T^{27} + \)\(90\!\cdots\!89\)\( T^{28} \)
|
| $41$
| \( 1 - 2 T + 310 T^{2} - 1067 T^{3} + 48772 T^{4} - 213511 T^{5} + 5293181 T^{6} - 25200647 T^{7} + 441132414 T^{8} - 2099126214 T^{9} + 29405656103 T^{10} - 134309132098 T^{11} + 1599620490390 T^{12} - 6841742496901 T^{13} + 71944474959847 T^{14} - 280511442372941 T^{15} + 2688962044345590 T^{16} - 9256719693326258 T^{17} + 83093356195269383 T^{18} - 243196788573553014 T^{19} + 2095424950583967774 T^{20} - 4907933707816401007 T^{21} + 42265654509203923901 T^{22} - 69899644194389007071 T^{23} + \)\(65\!\cdots\!72\)\( T^{24} - \)\(58\!\cdots\!47\)\( T^{25} + \)\(69\!\cdots\!10\)\( T^{26} - \)\(18\!\cdots\!42\)\( T^{27} + \)\(37\!\cdots\!61\)\( T^{28} \)
|
| $43$
| \( 1 - 12 T + 313 T^{2} - 2941 T^{3} + 46354 T^{4} - 364249 T^{5} + 4500456 T^{6} - 30371096 T^{7} + 323732139 T^{8} - 1907284425 T^{9} + 18605092085 T^{10} - 97945613665 T^{11} + 915170309538 T^{12} - 4461374153680 T^{13} + 40823650298033 T^{14} - 191839088608240 T^{15} + 1692149902335762 T^{16} - 7787361905663155 T^{17} + 63607107425290085 T^{18} - 280386913677400275 T^{19} + 2046428381248331811 T^{20} - 8255429132517363272 T^{21} + 52602231068531086056 T^{22} - \)\(18\!\cdots\!07\)\( T^{23} + \)\(10\!\cdots\!46\)\( T^{24} - \)\(27\!\cdots\!87\)\( T^{25} + \)\(12\!\cdots\!13\)\( T^{26} - \)\(20\!\cdots\!16\)\( T^{27} + \)\(73\!\cdots\!49\)\( T^{28} \)
|
| $47$
| \( 1 + 21 T + 642 T^{2} + 9579 T^{3} + 173282 T^{4} + 2058501 T^{5} + 28081277 T^{6} + 281260080 T^{7} + 3164831869 T^{8} + 27593886580 T^{9} + 267463992132 T^{10} + 2066070951610 T^{11} + 17645268146416 T^{12} + 121770185396311 T^{13} + 926763873038362 T^{14} + 5723198713626617 T^{15} + 38978397335432944 T^{16} + 214505684409005030 T^{17} + 1305138960590669892 T^{18} + 6328520110847306060 T^{19} + 34114404196032519901 T^{20} + \)\(14\!\cdots\!40\)\( T^{21} + \)\(66\!\cdots\!97\)\( T^{22} + \)\(23\!\cdots\!67\)\( T^{23} + \)\(91\!\cdots\!18\)\( T^{24} + \)\(23\!\cdots\!37\)\( T^{25} + \)\(74\!\cdots\!22\)\( T^{26} + \)\(11\!\cdots\!67\)\( T^{27} + \)\(25\!\cdots\!69\)\( T^{28} \)
|
| $53$
| \( 1 + 22 T + 600 T^{2} + 8891 T^{3} + 149025 T^{4} + 1767428 T^{5} + 23162405 T^{6} + 236054523 T^{7} + 2622232050 T^{8} + 23676784217 T^{9} + 231170051836 T^{10} + 1878471829095 T^{11} + 16435898992365 T^{12} + 121114546059821 T^{13} + 959063276750599 T^{14} + 6419070941170513 T^{15} + 46168440269553285 T^{16} + 279661250500176315 T^{17} + 1824042901780973116 T^{18} + 9901524448282933981 T^{19} + 58120098120237984450 T^{20} + \)\(27\!\cdots\!51\)\( T^{21} + \)\(14\!\cdots\!05\)\( T^{22} + \)\(58\!\cdots\!24\)\( T^{23} + \)\(26\!\cdots\!25\)\( T^{24} + \)\(82\!\cdots\!27\)\( T^{25} + \)\(29\!\cdots\!00\)\( T^{26} + \)\(57\!\cdots\!06\)\( T^{27} + \)\(13\!\cdots\!69\)\( T^{28} \)
|
| $59$
| \( 1 + 14 T + 581 T^{2} + 7377 T^{3} + 164702 T^{4} + 1883247 T^{5} + 30220988 T^{6} + 310284265 T^{7} + 4012968527 T^{8} + 37055439705 T^{9} + 408802361169 T^{10} + 3406965871622 T^{11} + 33055223215074 T^{12} + 249122296374202 T^{13} + 2161859424644700 T^{14} + 14698215486077918 T^{15} + 115065232011672594 T^{16} + 699719243747854738 T^{17} + 4953605787937155009 T^{18} + 26491834255233891795 T^{19} + \)\(16\!\cdots\!07\)\( T^{20} + \)\(77\!\cdots\!35\)\( T^{21} + \)\(44\!\cdots\!48\)\( T^{22} + \)\(16\!\cdots\!33\)\( T^{23} + \)\(84\!\cdots\!02\)\( T^{24} + \)\(22\!\cdots\!43\)\( T^{25} + \)\(10\!\cdots\!61\)\( T^{26} + \)\(14\!\cdots\!06\)\( T^{27} + \)\(61\!\cdots\!61\)\( T^{28} \)
|
| $61$
| \( 1 - 31 T + 799 T^{2} - 14275 T^{3} + 232164 T^{4} - 3132074 T^{5} + 39576049 T^{6} - 440162687 T^{7} + 4672193963 T^{8} - 45028609730 T^{9} + 421062079995 T^{10} - 3650714835224 T^{11} + 31205726643312 T^{12} - 251150250443459 T^{13} + 2015313166590698 T^{14} - 15320165277050999 T^{15} + 116116508839763952 T^{16} - 828642904013978744 T^{17} + 5829958610740050795 T^{18} - 38030997217130608730 T^{19} + \)\(24\!\cdots\!43\)\( T^{20} - \)\(13\!\cdots\!27\)\( T^{21} + \)\(75\!\cdots\!69\)\( T^{22} - \)\(36\!\cdots\!34\)\( T^{23} + \)\(16\!\cdots\!64\)\( T^{24} - \)\(62\!\cdots\!75\)\( T^{25} + \)\(21\!\cdots\!79\)\( T^{26} - \)\(50\!\cdots\!11\)\( T^{27} + \)\(98\!\cdots\!41\)\( T^{28} \)
|
| $67$
| \( 1 - 24 T + 645 T^{2} - 10579 T^{3} + 173398 T^{4} - 2229369 T^{5} + 27927266 T^{6} - 300633461 T^{7} + 3134279069 T^{8} - 29546445593 T^{9} + 270345477209 T^{10} - 2329683918478 T^{11} + 19689782826956 T^{12} - 162614886738420 T^{13} + 1334836555870912 T^{14} - 10895197411474140 T^{15} + 88387435110205484 T^{16} - 700682724373198714 T^{17} + 5447764423041301289 T^{18} - 39891398017718803451 T^{19} + \)\(28\!\cdots\!61\)\( T^{20} - \)\(18\!\cdots\!03\)\( T^{21} + \)\(11\!\cdots\!06\)\( T^{22} - \)\(60\!\cdots\!43\)\( T^{23} + \)\(31\!\cdots\!02\)\( T^{24} - \)\(12\!\cdots\!57\)\( T^{25} + \)\(52\!\cdots\!45\)\( T^{26} - \)\(13\!\cdots\!88\)\( T^{27} + \)\(36\!\cdots\!29\)\( T^{28} \)
|
| $71$
| \( 1 + 28 T + 793 T^{2} + 15570 T^{3} + 289339 T^{4} + 4536466 T^{5} + 66735100 T^{6} + 884178035 T^{7} + 11020890785 T^{8} + 127178786894 T^{9} + 1385246841317 T^{10} + 14162754693270 T^{11} + 137026427434000 T^{12} + 1252415837062688 T^{13} + 10846731641608785 T^{14} + 88921524431450848 T^{15} + 690750220694794000 T^{16} + 5069005695022958970 T^{17} + 35201450837805223877 T^{18} + \)\(22\!\cdots\!94\)\( T^{19} + \)\(14\!\cdots\!85\)\( T^{20} + \)\(80\!\cdots\!85\)\( T^{21} + \)\(43\!\cdots\!00\)\( T^{22} + \)\(20\!\cdots\!46\)\( T^{23} + \)\(94\!\cdots\!39\)\( T^{24} + \)\(35\!\cdots\!70\)\( T^{25} + \)\(13\!\cdots\!13\)\( T^{26} + \)\(32\!\cdots\!08\)\( T^{27} + \)\(82\!\cdots\!81\)\( T^{28} \)
|
| $73$
| \( 1 - 24 T + 559 T^{2} - 10259 T^{3} + 166212 T^{4} - 2371579 T^{5} + 31144574 T^{6} - 379413212 T^{7} + 4292139247 T^{8} - 45848681295 T^{9} + 466387972197 T^{10} - 4520665874695 T^{11} + 42080295557530 T^{12} - 377765144648286 T^{13} + 3289457070452829 T^{14} - 27576855559324878 T^{15} + 224245895026077370 T^{16} - 1758615876576224815 T^{17} + 13244598033951705477 T^{18} - 95047598769174952935 T^{19} + \)\(64\!\cdots\!83\)\( T^{20} - \)\(41\!\cdots\!64\)\( T^{21} + \)\(25\!\cdots\!94\)\( T^{22} - \)\(13\!\cdots\!27\)\( T^{23} + \)\(71\!\cdots\!88\)\( T^{24} - \)\(32\!\cdots\!43\)\( T^{25} + \)\(12\!\cdots\!39\)\( T^{26} - \)\(40\!\cdots\!92\)\( T^{27} + \)\(12\!\cdots\!09\)\( T^{28} \)
|
| $79$
| \( 1 - 65 T + 2695 T^{2} - 81273 T^{3} + 1994435 T^{4} - 41257851 T^{5} + 745630895 T^{6} - 11965350812 T^{7} + 173460480090 T^{8} - 2292541231594 T^{9} + 27902035275023 T^{10} - 314417424571610 T^{11} + 3300424334374354 T^{12} - 32356362354243161 T^{13} + 297156786296087190 T^{14} - 2556152625985209719 T^{15} + 20597948270830343314 T^{16} - \)\(15\!\cdots\!90\)\( T^{17} + \)\(10\!\cdots\!63\)\( T^{18} - \)\(70\!\cdots\!06\)\( T^{19} + \)\(42\!\cdots\!90\)\( T^{20} - \)\(22\!\cdots\!08\)\( T^{21} + \)\(11\!\cdots\!95\)\( T^{22} - \)\(49\!\cdots\!69\)\( T^{23} + \)\(18\!\cdots\!35\)\( T^{24} - \)\(60\!\cdots\!67\)\( T^{25} + \)\(15\!\cdots\!95\)\( T^{26} - \)\(30\!\cdots\!35\)\( T^{27} + \)\(36\!\cdots\!81\)\( T^{28} \)
|
| $83$
| \( 1 - 15 T + 316 T^{2} - 3384 T^{3} + 55867 T^{4} - 540953 T^{5} + 8059014 T^{6} - 79440974 T^{7} + 1044683618 T^{8} - 9433281291 T^{9} + 111583188986 T^{10} - 972398968994 T^{11} + 10784971542554 T^{12} - 91456205304469 T^{13} + 961321029078984 T^{14} - 7590865040270927 T^{15} + 74297668956654506 T^{16} - 556005089284172278 T^{17} + 5295550801101252506 T^{18} - 37158078402100510113 T^{19} + \)\(34\!\cdots\!42\)\( T^{20} - \)\(21\!\cdots\!98\)\( T^{21} + \)\(18\!\cdots\!74\)\( T^{22} - \)\(10\!\cdots\!59\)\( T^{23} + \)\(86\!\cdots\!83\)\( T^{24} - \)\(43\!\cdots\!28\)\( T^{25} + \)\(33\!\cdots\!76\)\( T^{26} - \)\(13\!\cdots\!45\)\( T^{27} + \)\(73\!\cdots\!29\)\( T^{28} \)
|
| $89$
| \( 1 - 11 T + 637 T^{2} - 4666 T^{3} + 194340 T^{4} - 988871 T^{5} + 40302057 T^{6} - 140952095 T^{7} + 6481748951 T^{8} - 15564145255 T^{9} + 861119774688 T^{10} - 1481669315671 T^{11} + 96912973093927 T^{12} - 132503710750456 T^{13} + 9321434523205205 T^{14} - 11792830256790584 T^{15} + 767647659876995767 T^{16} - 1044530935799269199 T^{17} + 54028584433340195808 T^{18} - 86911112376791264495 T^{19} + \)\(32\!\cdots\!11\)\( T^{20} - \)\(62\!\cdots\!55\)\( T^{21} + \)\(15\!\cdots\!17\)\( T^{22} - \)\(34\!\cdots\!39\)\( T^{23} + \)\(60\!\cdots\!40\)\( T^{24} - \)\(12\!\cdots\!74\)\( T^{25} + \)\(15\!\cdots\!77\)\( T^{26} - \)\(24\!\cdots\!59\)\( T^{27} + \)\(19\!\cdots\!41\)\( T^{28} \)
|
| $97$
| \( 1 - 23 T + 725 T^{2} - 11408 T^{3} + 224098 T^{4} - 2793230 T^{5} + 41901368 T^{6} - 415274078 T^{7} + 5095591937 T^{8} - 38237772108 T^{9} + 402889459893 T^{10} - 1768490206825 T^{11} + 18928181782076 T^{12} + 18318177648168 T^{13} + 831994608674812 T^{14} + 1776863231872296 T^{15} + 178095262387553084 T^{16} - 1614053262533593225 T^{17} + 35667514206805626933 T^{18} - \)\(32\!\cdots\!56\)\( T^{19} + \)\(42\!\cdots\!73\)\( T^{20} - \)\(33\!\cdots\!14\)\( T^{21} + \)\(32\!\cdots\!48\)\( T^{22} - \)\(21\!\cdots\!10\)\( T^{23} + \)\(16\!\cdots\!02\)\( T^{24} - \)\(81\!\cdots\!24\)\( T^{25} + \)\(50\!\cdots\!25\)\( T^{26} - \)\(15\!\cdots\!71\)\( T^{27} + \)\(65\!\cdots\!69\)\( T^{28} \)
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