A191351 E.g.f. (1+x+x^2)^(x+x^2)

1, 0, 2, 9, 8, 130, 1134, -252, 29504, 447480, -1837800, 14172840, 471846792, -4864408848, 14099478288, 1166776034760, -18687216197760, 31767501808320, 5630793922569024, -113411010324632832, 156669582211562880

Offset

0,3

Links

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

Formula

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

Mathematica

With[{nn=20}, CoefficientList[Series[(1+x+x^2)^(x+x^2), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Aug 21 2017 *)

Prog

(Maxima)
a(n):=(sum(sum((binomial(k, n-k)*stirling1(k-m, m))/(k-m)!, k, m, n), m, 1, n))*n!;

Crossrefs

Sequence in context: A351166 A092270 A249225 * A324553 A230283 A121067

Adjacent sequences: A191348 A191349 A191350 * A191352 A191353 A191354

Keyword

sign

Author

Vladimir Kruchinin, May 31 2011

Status

approved