A376443 Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x*(exp(x^2) - 1))^2 ).
1, 0, 0, 12, 0, 120, 10800, 1680, 766080, 55913760, 48686400, 12973625280, 878369184000, 2257312337280, 475877474392320, 31178226637958400, 176135891323392000, 32566007822802854400, 2111180034178805990400, 22027962609483730099200, 3749400628293386626560000, 244391453278125083388057600
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x*(exp(x^2)-1))^2)/x)) -
PARI
a(n) = 2*n!*sum(k=0, n\2, (3*n-2*k+1)!*stirling(k, n-2*k, 2)/k!)/(2*n+2)!;
Formula
E.g.f. A(x) satisfies A(x) = 1/(1 - x*A(x) * (exp(x^2*A(x)^2) - 1))^2.
a(n) = (2 * n!/(2n+2)!) * Sum_{k=0..floor(n/2)} (3*n-2*k+1)! * Stirling2(k,n-2*k)/k!.