A376441 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 + x*log(1-x^2))^2 ).
1, 0, 0, 12, 0, 120, 10800, 3360, 766080, 56064960, 76507200, 12988926720, 885913459200, 3162288729600, 477701680135680, 31728803730624000, 230820218044416000, 32828647402065715200, 2173902177236319129600, 27658882036996206796800, 3801535675181689116672000, 255228267875636473786368000
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))^2)/x)) -
PARI
a(n) = 2*n!*sum(k=0, n\2, (3*n-2*k+1)!*abs(stirling(k, n-2*k, 1))/k!)/(2*n+2)!;
Formula
E.g.f. A(x) satisfies A(x) = 1/(1 + x*A(x) * log(1 - x^2*A(x)^2))^2.
a(n) = (2 * n!/(2n+2)!) * Sum_{k=0..floor(n/2)} (3*n-2*k+1)! * |Stirling1(k,n-2*k)|/k!.