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A003017 Expansion of 1/(1 - x*exp(x) + x^2*exp(2*x) - x^3*exp(3*x)). 0

%I #17 Oct 30 2022 10:03:41

%S 1,1,2,3,28,605,9366,116767,1310408,15812505,263924650,6018875291,

%T 148630870092,3548481410773,82543469312318,2000101425252855,

%U 54347539111582096,1678367049470539697,56020955060945897298

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

%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) = 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

%o (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 */

%K nonn

%O 0,3

%A _N. J. A. Sloane_

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Last modified June 14 14:51 EDT 2024. Contains 373400 sequences. (Running on oeis4.)