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A189487 Expansion of e.g.f. exp(x*exp(x) + x^2*exp(2*x)).

%I A189487 #23 Jul 17 2023 04:34:38
%S A189487 1,1,5,28,185,1456,13267,135598,1528193,18805240,250522451,3585332554,
%T A189487 54774501025,888739031116,15249006695483,275641537989766,
%U A189487 5231788966650113,103968303762747472,2157673505603964643,46656574558459795522,1049037051211541521121
%N A189487 Expansion of e.g.f. exp(x*exp(x) + x^2*exp(2*x)).
%H A189487 Seiichi Manyama, <a href="/A189487/b189487.txt">Table of n, a(n) for n = 0..476</a>
%H A189487 Vladimir Kruchinin and D. V. Kruchinin, <a href="http://arxiv.org/abs/1103.2582">Composita and their properties</a>, arXiv:1103.2582 [math.CO], 2011-2013.
%F A189487 a(n) = n!*sum(m=1..n, sum(k=m..n, (k^(n-k)*binomial(m,k-m))/(n-k)!)/m!), n>0, a(0)=1.
%t A189487 With[{nn=30},CoefficientList[Series[Exp[x Exp[x]+x^2 Exp[2x]],{x,0,nn}], x]Range[0,nn]!] (* _Harvey P. Dale_, Sep 22 2011 *)
%o A189487 (Maxima)
%o A189487 a(n):=n!*sum(sum((k^(n-k)*binomial(m,k-m))/(n-k)!,k,m,n)/m!,m,1,n);
%o A189487 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x*exp(x)+x^2*exp(2*x)))) \\ _Seiichi Manyama_, Jul 17 2023
%Y A189487 Cf. A060905.
%K A189487 nonn
%O A189487 0,3
%A A189487 _Vladimir Kruchinin_, Apr 23 2011
%E A189487 More terms from _Harvey P. Dale_, Sep 22 2011