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

1, 1, 5, 28, 185, 1456, 13267, 135598, 1528193, 18805240, 250522451, 3585332554, 54774501025, 888739031116, 15249006695483, 275641537989766, 5231788966650113, 103968303762747472, 2157673505603964643, 46656574558459795522, 1049037051211541521121

Offset: 0

Author

Vladimir Kruchinin, Apr 23 2011

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..476
• Vladimir Kruchinin and D. V. Kruchinin, Composita and their properties, arXiv:1103.2582 [math.CO], 2011-2013.

Crossrefs

Cf. A060905.

Programs

Mathematica

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 *)

Maxima

a(n):=n!*sum(sum((k^(n-k)*binomial(m,k-m))/(n-k)!,k,m,n)/m!,m,1,n);

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

Formula

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.

Extensions

More terms from Harvey P. Dale, Sep 22 2011