A003017 Expansion of 1/(1 - x*exp(x) + x^2*exp(2*x) - x^3*exp(3*x)).

1, 1, 2, 3, 28, 605, 9366, 116767, 1310408, 15812505, 263924650, 6018875291, 148630870092, 3548481410773, 82543469312318, 2000101425252855, 54347539111582096, 1678367049470539697, 56020955060945897298

Offset

0,3

Links

Table of n, a(n) for n=0..18.

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

Formula

a(n) = sum(sum(k^(n-k)/(n-k)!*sum(binomial(j,k-3*m+2*j)*(-1)^(k-3*m+2*j)*binomial(m,j),j,0,m),k,m,n),m,1,n), n>0. - Vladimir Kruchinin, Aug 20 2010

Prog

(Maxima) a(n):=sum(sum(k^(n-k)/(n-k)!*sum(binomial(j, k-3*m+2*j)*(-1)^(k-3*m+2*j)*binomial(m, j), j, 0, m), k, m, n), m, 1, n); /* Vladimir Kruchinin, Aug 20 2010 */

Crossrefs

Sequence in context: A219975 A319146 A206591 * A096580 A371024 A351693

Adjacent sequences: A003014 A003015 A003016 * A003018 A003019 A003020

Keyword

nonn

Author

N. J. A. Sloane

Status

approved