A377830 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x)/(1 + x)^3 ).
1, 4, 45, 886, 25397, 963216, 45615553, 2595412240, 172624541769, 13150155923200, 1129371806449301, 107987110491257856, 11379014255782146685, 1310277285293012678656, 163703077517048727256425, 22057132253723442887059456, 3188342874266180285119069457, 492178313447920665621400780800
Offset: 0
Keywords
Programs
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PARI
a(n) = n!*sum(k=0, n, (n+1)^(k-1)*binomial(3*n+3, n-k)/k!);
Formula
E.g.f. A(x) satisfies A(x) = (1 + x*A(x))^3 * exp(x * A(x)).
a(n) = n! * Sum_{k=0..n} (n+1)^(k-1) * binomial(3*n+3,n-k)/k!.