A367161
E.g.f. satisfies A(x) = 1 + A(x)^3 * (exp(x) - 1).
Original entry on oeis.org
1, 1, 7, 91, 1795, 47851, 1612027, 65731891, 3148530595, 173319612571, 10782796483147, 748237171338691, 57299882326956595, 4800323120225595691, 436719009263680421467, 42878536726317406241491, 4519124182661042439577795, 508885588456024192452993211
Offset: 0
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Table[Sum[(3*k)!/(2*k+1)! * StirlingS2[n,k], {k,0,n}], {n,0,20}] (* Vaclav Kotesovec, Nov 10 2023 *)
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a(n) = sum(k=0, n, (3*k)!/(2*k+1)!*stirling(n, k, 2));
A367155
E.g.f. satisfies A(x) = 1 + A(x)^3 * log(1 + x).
Original entry on oeis.org
1, 1, 5, 56, 948, 21804, 634284, 22348584, 925322784, 44039346264, 2369167375656, 142173632632272, 9416315321258928, 682290228636729504, 53689645309437175968, 4559660591348115191808, 415683140400707316145920, 40490500091575002629253120
Offset: 0
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Table[Sum[(3*k)!/(2*k+1)! * StirlingS1[n,k], {k,0,n}], {n,0,20}] (* Vaclav Kotesovec, Nov 10 2023 *)
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a(n) = sum(k=0, n, (3*k)!/(2*k+1)!*stirling(n, k, 1));
A367164
E.g.f. satisfies A(x) = 1 + A(x)^3 * (1 - exp(-x)).
Original entry on oeis.org
1, 1, 5, 55, 929, 21271, 616265, 21624415, 891671009, 42263854471, 2264336600825, 135325966276975, 8926057815521489, 644116254555006871, 50477965058305364585, 4269330999037434100735, 387619447676360230226369, 37602089272441407334114471
Offset: 0
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Table[Sum[(-1)^(n-k) * (3*k)!/(2*k+1)! * StirlingS2[n,k], {k,0,n}], {n,0,20}] (* Vaclav Kotesovec, Nov 10 2023 *)
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a(n) = sum(k=0, n, (-1)^(n-k)*(3*k)!/(2*k+1)!*stirling(n, k, 2));
A371141
E.g.f. satisfies A(x) = 1 - x*A(x)^3 * log(1 - x).
Original entry on oeis.org
1, 0, 2, 3, 80, 390, 10764, 104160, 3162144, 48889008, 1647798480, 35939566080, 1347110453952, 38272507827840, 1593399505840128, 55860824012535360, 2575479834957911040, 107239963351030433280, 5453101063482843276288, 262319113586136087567360
Offset: 0
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a(n) = n!*sum(k=0, n\2, (3*k)!/(2*k+1)!*abs(stirling(n-k, k, 1))/(n-k)!);
A377445
E.g.f. satisfies A(x) = 1/(1 + A(x) * log(1 - x))^2.
Original entry on oeis.org
1, 2, 16, 226, 4678, 128728, 4437416, 184176816, 8949477600, 498611374704, 31343763192144, 2194986671431200, 169478318264408832, 14304849733469090976, 1310439414650613267552, 129495512412669053694720, 13731040497246647099309568, 1555129289690056322821075968
Offset: 0
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Table[2*Sum[(3*k+1)!/(2*k+2)! * Abs[StirlingS1[n,k]], {k,0,n}], {n,0,20}] (* Vaclav Kotesovec, Aug 27 2025 *)
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a(n) = 2*sum(k=0, n, (3*k+1)!/(2*k+2)!*abs(stirling(n, k, 1)));
A377448
E.g.f. satisfies A(x) = 1/(1 + A(x)^4 * log(1 - x)).
Original entry on oeis.org
1, 1, 11, 242, 8216, 379874, 22286230, 1586307120, 132837129240, 12796759555080, 1394232748385400, 169520552541195360, 22755571384758552000, 3342628991206830087840, 533345016648993065361120, 91858353520083403370288640, 16985334194077245970016972160, 3356121850436121636865113624960
Offset: 0
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a(n) = sum(k=0, n, (5*k)!/(4*k+1)!*abs(stirling(n, k, 1)));
A377447
E.g.f. satisfies A(x) = 1/(1 + A(x)^3 * log(1 - x)).
Original entry on oeis.org
1, 1, 9, 158, 4246, 154924, 7162292, 401410680, 26453842848, 2004890580840, 171808440737928, 16427634731841552, 1733913231506623632, 200249346295125726624, 25118871041680870112352, 3400884689353492497349248, 494317826168209713209318400, 76773315675375252953433141120
Offset: 0
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a(n) = sum(k=0, n, (4*k)!/(3*k+1)!*abs(stirling(n, k, 1)));
A377693
E.g.f. satisfies A(x) = (1 - log(1 - x) * A(x))^3.
Original entry on oeis.org
1, 3, 27, 408, 8814, 249702, 8789946, 370639896, 18233312640, 1025931258264, 65016004033944, 4583861319427200, 355955157532869552, 30192068409536580336, 2777615578746538933392, 275502517287785484635520, 29308962522270448504338048, 3329136621436554585165282048
Offset: 0
-
a(n) = 3*sum(k=0, n, (3*k+2)!/(2*k+3)!*abs(stirling(n, k, 1)));
Showing 1-8 of 8 results.