A007116 Expansion of e.g.f. (1+x)^(exp(x)).

1, 1, 2, 6, 18, 75, 295, 1575, 7196, 48993, 230413, 2164767, 8055938, 139431149, 70125991, 14201296057, -77573062280, 2389977322593, -28817693086263, 615493949444827, -10403976760589602, 215611836994976237

Offset: 0

Author

Simon Plouffe

Keywords

• sign
• easy

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..451

Crossrefs

Cf. A002741, A009198, A191365.

Programs

Mathematica

With[{nn=25},CoefficientList[Series[(1+x)^Exp[x],{x,0,nn}], x] Range[ 0,nn]!] (* Harvey P. Dale, Sep 21 2011 *)

Maxima

a(n):=sum(sum(binomial(n,i)*k^i*stirling1(n-i,k),i,0,n-k),k,1,n); /* Vladimir Kruchinin, Jun 01 2011 */

Formula

a(n) = sum(k=1..n, sum(i=0..n-k, binomial(n,i)*k^i*Stirling1(n-i,k))), n>0, a(0)=1. - Vladimir Kruchinin, Jun 01 2011

|a(n)| ~ n!/(Gamma(-exp(-1))*n^(1+exp(-1))). - Vaclav Kotesovec, Jun 27 2013

Extensions

Definition and terms corrected, and more terms added by Joerg Arndt, Jun 01 2011