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A191365 Expansion of e.g.f. (1/(1-x))^exp(x).

%I A191365 #21 May 03 2022 11:05:45
%S A191365 1,1,4,18,102,695,5485,49077,490308,5404569,65106103,850535477,
%T A191365 11972432846,180605413001,2906109200293,49678357272247,
%U A191365 898988188301320,17167497793440977,344991795682802331,7277230501449340417,160765066207998479698
%N A191365 Expansion of e.g.f. (1/(1-x))^exp(x).
%C A191365 Exponential transform of A002104. - _Seiichi Manyama_, May 03 2022
%H A191365 Seiichi Manyama, <a href="/A191365/b191365.txt">Table of n, a(n) for n = 0..448</a>
%F A191365 a(n) = sum(k=1..n, sum(i=0..n-k, binomial(n,i)*k^i*(-1)^(n-k-i)*Stirling1(n-i,k))), n>0, a(0)=1.
%F A191365 a(n) ~ n! * n^(exp(1)-1)/Gamma(exp(1)) * (1-exp(1)*(exp(1)-1)*log(n)/n). - _Vaclav Kotesovec_, Jun 21 2013
%F A191365 a(0) = 1; a(n) = Sum_{k=1..n} A002104(k) * binomial(n-1,k-1) * a(n-k). - _Seiichi Manyama_, May 03 2022
%t A191365 CoefficientList[Series[(1/(1-x))^Exp[x], {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Jun 21 2013 *)
%o A191365 (Maxima) a(n):=sum(sum(binomial(n,i)*k^i*(-1)^(n-k-i)*stirling1(n-i,k),i,0,n-k),k,1,n);
%o A191365 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-x)^exp(x))) \\ _Seiichi Manyama_, May 03 2022
%Y A191365 Cf. A002104, A298374.
%K A191365 nonn
%O A191365 0,3
%A A191365 _Vladimir Kruchinin_, May 31 2011