A377967 Expansion of e.g.f. (1+x)^3 * exp(x*(1+x)^3).
1, 4, 19, 124, 961, 8236, 79339, 840484, 9595009, 117764596, 1542837091, 21406165804, 313381177729, 4822681240924, 77704955681851, 1307128152596116, 22899018541506049, 416756647023727204, 7863586717014612019, 153550319029835965276, 3097694623619639050561
Offset: 0
Programs
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Mathematica
With[{nn=20},CoefficientList[Series[(1+x)^3 Exp[x*(1+x)^3],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, May 28 2025 *) -
PARI
a(n, s=3, 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+3,n-k) / k!.