A007116 Expansion of e.g.f. (1+x)^(exp(x)). (Formerly M1634)

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

Offset

0,3

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

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

Mathematica

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

Prog

(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 */

Crossrefs

Cf. A002741, A009198, A191365.

Sequence in context: A277862 A213427 A006388 * A280763 A079391 A162058

Adjacent sequences: A007113 A007114 A007115 * A007117 A007118 A007119

Keyword

sign,easy

Author

Simon Plouffe

Extensions

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

Status

approved