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%I M1634 #38 May 27 2022 10:14:07
%S 1,1,2,6,18,75,295,1575,7196,48993,230413,2164767,8055938,139431149,
%T 70125991,14201296057,-77573062280,2389977322593,-28817693086263,
%U 615493949444827,-10403976760589602,215611836994976237
%N Expansion of e.g.f. (1+x)^(exp(x)).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Seiichi Manyama, <a href="/A007116/b007116.txt">Table of n, a(n) for n = 0..451</a>
%F 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
%F |a(n)| ~ n!/(Gamma(-exp(-1))*n^(1+exp(-1))). - _Vaclav Kotesovec_, Jun 27 2013
%t With[{nn=25},CoefficientList[Series[(1+x)^Exp[x],{x,0,nn}], x] Range[ 0,nn]!] (* _Harvey P. Dale_, Sep 21 2011 *)
%o (Maxima)
%o 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 */
%Y Cf. A002741, A009198, A191365.
%K sign,easy
%O 0,3
%A _Simon Plouffe_
%E Definition and terms corrected, and more terms added by _Joerg Arndt_, Jun 01 2011
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