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A189488 Expansion of e.g.f. exp(x*exp(x)+x^2*exp(2*x)+x^3*exp(3*x)). 1

%I #16 Oct 30 2022 09:40:03

%S 1,1,5,34,281,2656,28867,359038,5002097,76499128,1269310931,

%T 22704893674,435561243625,8912650794412,193534333139435,

%U 4440414121757926,107270144994315233,2720370239752704592,72227750784404889187,2002807470702054148930,57871801203185571969881

%N Expansion of e.g.f. exp(x*exp(x)+x^2*exp(2*x)+x^3*exp(3*x)).

%H Harvey P. Dale, <a href="/A189488/b189488.txt">Table of n, a(n) for n = 0..449</a>

%H 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 a(n) = n!*sum(m=1..n, sum(k=m..n,(k^(n-k)*sum(j=0..m, binomial(j,-3*m+k+2*j)*binomial(m,j)))/(n-k)!)/m!), n>0, a(0)=1.

%t With[{nn=20},CoefficientList[Series[Exp[x*Exp[x]+x^2 Exp[2x]+x^3 Exp[3x]],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Mar 07 2016 *)

%o (Maxima)

%o a(n):=n!*sum(sum((k^(n-k)*sum(binomial(j,-3*m+k+2*j)*binomial(m,j),j,0,m))/(n-k)!,k,m,n)/m!,m,1,n);

%K nonn

%O 0,3

%A _Vladimir Kruchinin_, Apr 23 2011

%E More terms from _Harvey P. Dale_, Mar 07 2016

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)