A202152 Expansion of e.g.f.: exp(x*(1+x)^x).

1, 1, 1, 7, 13, 101, 361, 2269, 18201, 48817, 1436401, -2283269, 157443397, -826037939, 21355181849, -160556822999, 3084325024561, -22223879489055, 291212769688417, 2180748026158255, -118745486165378819, 4884619264768661461, -140063412525642293687, 4020051993317128467029

Offset: 0

Author

Vladimir Kruchinin, Dec 12 2011

Keywords

• sign

Programs

Mathematica

With[{nn=30},CoefficientList[Series[Exp[x (1+x)^x],{x,0,nn}],x] Range[ 0,nn]!] (* Harvey P. Dale, Oct 13 2019 *)

Maxima

a(n):=if n=0 then 1 else n!*sum(sum((m^k*stirling1(n-m-k,k))/(n-m-k)!,k,0,n-m)/m!,m,1,n);

Formula

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

Extensions

Definition clarified by Harvey P. Dale, Oct 13 2019