A191423 Expansion of e.g.f.: (1+x+x^2+x^3)^x

1, 0, 2, 3, 20, -30, 594, -840, 14384, -167832, 2300040, -17190360, 153272712, -2775904560, 51294972624, -651268374120, 7597950113280, -151775259773760, 3587640413505984, -63586583168595840, 972086975299451520

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Formula

a(n)=(sum(m=1..n, sum(k=0..n-2*m, (stirling1(m+k,m)*sum(j=0..m+k, binomial(j,n-3*(m+k)-m+2*j)*binomial(m+k,j)))/(m+k)!)))*n!, n>0, a(0)=1.

Mathematica

With[{nn=30}, CoefficientList[Series[(1+x+x^2+x^3)^x, {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, Apr 01 2019 *)

Prog

(Maxima)
a(n):=(sum(sum((stirling1(m+k, m)*sum(binomial(j, n-3*(m+k)-m+2*j)*binomial(m+k, j), j, 0, m+k))/(m+k)!, k, 0, n-2*m), m, 1, n))*n!;

Crossrefs

Sequence in context: A042781 A308885 A136886 * A195686 A295365 A233410

Adjacent sequences: A191420 A191421 A191422 * A191424 A191425 A191426

Keyword

sign

Author

Vladimir Kruchinin, Jun 02 2011

Extensions

Definition clarified by Harvey P. Dale, Apr 01 2019

Status

approved