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

1, 1, 5, 34, 281, 2656, 28867, 359038, 5002097, 76499128, 1269310931, 22704893674, 435561243625, 8912650794412, 193534333139435, 4440414121757926, 107270144994315233, 2720370239752704592, 72227750784404889187, 2002807470702054148930, 57871801203185571969881

Offset

0,3

Links

Harvey P. Dale, Table of n, a(n) for n = 0..449

Vladimir Kruchinin and D. V. Kruchinin, Composita and their properties, arXiv:1103.2582 [math.CO], 2011-2013.

Formula

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.

Mathematica

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 *)

Prog

(Maxima)
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);

Crossrefs

Sequence in context: A292877 A257887 A090367 * A111557 A211794 A289147

Adjacent sequences: A189485 A189486 A189487 * A189489 A189490 A189491

Keyword

nonn

Author

Vladimir Kruchinin, Apr 23 2011

Extensions

More terms from Harvey P. Dale, Mar 07 2016

Status

approved