A376442 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 + x*log(1-x^2))^3 ).
1, 0, 0, 18, 0, 180, 23760, 5040, 1693440, 180260640, 169646400, 42116215680, 4148153856000, 10311946444800, 2266331900152320, 215416210961952000, 1103951255139532800, 227420391096138240000, 21290356810886504140800, 193675502529294757171200, 38377888101603670523904000
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1+x*log(1-x^2))^3)/x)) -
PARI
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)!;
Formula
E.g.f. A(x) satisfies A(x) = 1/(1 + x*A(x) * log(1 - x^2*A(x)^2))^3.
a(n) = (3 * n!/(3n+3)!) * Sum_{k=0..floor(n/2)} (4*n-2*k+2)! * |Stirling1(k,n-2*k)|/k!.