A375680
Expansion of e.g.f. 1 / (1 + x * log(1 - x^2))^2.
Original entry on oeis.org
1, 0, 0, 12, 0, 120, 2160, 3360, 120960, 1632960, 9979200, 255467520, 3592512000, 45664819200, 1070840010240, 18027225216000, 340344048844800, 8174882722406400, 169308486085939200, 4019018956285132800, 104511967278630912000, 2606273308503760896000
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x*log(1-x^2))^2))
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a(n) = n!*sum(k=0, n\2, (n-2*k+1)!*abs(stirling(k, n-2*k, 1))/k!);
A375807
Expansion of e.g.f. 1/(1 + (log(1 - x^2))/x)^3.
Original entry on oeis.org
1, 3, 12, 69, 504, 4440, 45720, 538020, 7116480, 104455008, 1684005120, 29571696000, 561695238720, 11472451848000, 250694772007680, 5835284153899200, 144124039400140800, 3764378233282867200, 103661897106414366720, 3001493647870874956800
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1+log(1-x^2)/x)^3))
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a(n) = n!*sum(k=0, n\2, (n-2*k+2)!*abs(stirling(n-k, n-2*k, 1))/(n-k)!)/2;
A376442
Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 + x*log(1-x^2))^3 ).
Original entry on oeis.org
1, 0, 0, 18, 0, 180, 23760, 5040, 1693440, 180260640, 169646400, 42116215680, 4148153856000, 10311946444800, 2266331900152320, 215416210961952000, 1103951255139532800, 227420391096138240000, 21290356810886504140800, 193675502529294757171200, 38377888101603670523904000
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1+x*log(1-x^2))^3)/x))
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a(n) = 3*n!*sum(k=0, n\2, (4*n-2*k+2)!*abs(stirling(k, n-2*k, 1))/k!)/(3*n+3)!;
Showing 1-3 of 3 results.