A377966 Expansion of e.g.f. (1+x)^2 * exp(x*(1+x)^3).
1, 3, 13, 85, 621, 5131, 48553, 500613, 5590105, 67453651, 868300581, 11854859413, 171122864773, 2598083998875, 41331779697601, 687151457132101, 11904595227392433, 214378528158055843, 4004773210169606845, 77459628036613435221, 1548502062887370346141
Offset: 0
Programs
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PARI
a(n, s=2, t=3) = n!*sum(k=0, n, binomial(t*k+s, n-k)/k!);
Formula
a(n) = n! * Sum_{k=0..n} binomial(3*k+2,n-k) / k!.