This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A007116 M1634 #38 May 27 2022 10:14:07
%S A007116 1,1,2,6,18,75,295,1575,7196,48993,230413,2164767,8055938,139431149,
%T A007116 70125991,14201296057,-77573062280,2389977322593,-28817693086263,
%U A007116 615493949444827,-10403976760589602,215611836994976237
%N A007116 Expansion of e.g.f. (1+x)^(exp(x)).
%D A007116 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A007116 Seiichi Manyama, <a href="/A007116/b007116.txt">Table of n, a(n) for n = 0..451</a>
%F A007116 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 A007116 |a(n)| ~ n!/(Gamma(-exp(-1))*n^(1+exp(-1))). - _Vaclav Kotesovec_, Jun 27 2013
%t A007116 With[{nn=25},CoefficientList[Series[(1+x)^Exp[x],{x,0,nn}], x] Range[ 0,nn]!] (* _Harvey P. Dale_, Sep 21 2011 *)
%o A007116 (Maxima)
%o A007116 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 A007116 Cf. A002741, A009198, A191365.
%K A007116 sign,easy
%O A007116 0,3
%A A007116 _Simon Plouffe_
%E A007116 Definition and terms corrected, and more terms added by _Joerg Arndt_, Jun 01 2011