A375661
Expansion of e.g.f. 1 / (1 - x * (exp(x) - 1))^3.
Original entry on oeis.org
1, 0, 6, 9, 156, 735, 9738, 83181, 1129656, 13662459, 207281190, 3151269033, 54457383060, 980680471095, 19240001086530, 397345461622245, 8763618490102128, 203472380293912563, 4991552271140255838, 128517790560854181537, 3472936316648987980620
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-x*(exp(x)-1))^3))
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a(n) = n!*sum(k=0, n\2, (k+2)!*stirling(n-k, k, 2)/(n-k)!)/2;
A375671
Expansion of e.g.f. 1 / (1 + x * log(1 - x))^2.
Original entry on oeis.org
1, 0, 4, 6, 88, 420, 5148, 44520, 587424, 7203168, 109106640, 1689621120, 29620245312, 546547098240, 10989238893696, 233884517368320, 5324618721070080, 128058198711690240, 3260308438558826496, 87336328336058603520, 2459915920512955929600
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x*log(1-x))^2))
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a(n) = n!*sum(k=0, n\2, (k+1)!*abs(stirling(n-k, k, 1))/(n-k)!);
A376381
Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x*(exp(x) - 1))^2 ).
Original entry on oeis.org
1, 0, 4, 6, 272, 1570, 63912, 792554, 33262784, 684763650, 30981768680, 915838324522, 45524048263872, 1765020653500130, 97096528136899592, 4651295721203951850, 283478019364268181632, 16107548441248677913858, 1084981357752210351649512, 71056829948555342150405354, 5267564532376249471978526720
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x*(exp(x)-1))^2)/x))
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a(n) = 2*n!*sum(k=0, n\2, (2*n+k+1)!*stirling(n-k, k, 2)/(n-k)!)/(2*n+2)!;
A377646
Expansion of e.g.f. (1 + x * (exp(x) - 1))^2.
Original entry on oeis.org
1, 0, 4, 6, 32, 130, 432, 1274, 3488, 9090, 22880, 56122, 134928, 319202, 745136, 1719930, 3931712, 8912386, 20053440, 44825978, 99614000, 220200162, 484441232, 1061157946, 2315254752, 5033163650, 10905189152, 23555209914, 50734299728, 108984793570
Offset: 0
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a(n) = n!*sum(k=0, n\2, k!*binomial(2, k)*stirling(n-k, k, 2)/(n-k)!);
Showing 1-4 of 4 results.