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

0,4

Links

Table of n, a(n) for n=0..23.

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.

Mathematica

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

Prog

(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)

Crossrefs

Sequence in context: A253333 A039687 A001544 * A136720 A323468 A035030

Adjacent sequences: A202149 A202150 A202151 * A202153 A202154 A202155

Keyword

sign

Author

Vladimir Kruchinin, Dec 12 2011

Extensions

Definition clarified by Harvey P. Dale, Oct 13 2019

Status

approved