|
%I #12 Nov 12 2017 06:16:47
%S 1,1,6,52,602,8223,128917,2273716,44509914,957408649,22449011336,
%T 570032756328,15587503694363,456793916757139,14284890417759141,
%U 474896318288651220,16726743380843538668,622282429409944248297,24385251974172090147514,1004017088910699487855180
%N Row sums of A291844.
%H Gheorghe Coserea, <a href="/A294158/b294158.txt">Table of n, a(n) for n = 0..202</a>
%H Luca G. Molinari, Nicola Manini, <a href="https://arxiv.org/abs/cond-mat/0512342">Enumeration of many-body skeleton diagrams</a>, arXiv:cond-mat/0512342 [cond-mat.str-el], 2006.
%F a(n) = Sum_{k=0..floor((2*n-1)/3)} A291844(n,k), n > 0.
%o (PARI)
%o A291843_ser(N, t='t) = {
%o my(x='x+O('x^N), y=1, y1=0, n=1,
%o dn = 1/(-2*t^2*x^4 - (2*t^2+3*t)*x^3 - (2*t+1)*x^2 + (2*t-1)*x + 1));
%o while (n++,
%o y1 = (2*x^2*y'*((-t^2 + t)*x + (-t + 1) + (t^2*x^2 + (t^2 + t)*x + t)*y) +
%o (t*x^2 + t*x)*y^2 - (2*t^2*x^3 + 3*t*x^2 + (-t + 1)*x - 1))*dn;
%o if (y1 == y, break); y = y1;); y;
%o };
%o A291844_ser(N, t='t) = {
%o my(z = A291843_ser(N+1,t));
%o ((1+x)*z - 1)*(1 + t*x)/((1-t + t*(1+x)*z)*x*z^2);
%o };
%o Vec(A291844_ser(20,t=1))
%Y Cf. A049464(y), A287039(x), A286799(z), A287029(u), A291844.
%K nonn
%O 0,3
%A _Gheorghe Coserea_, Oct 24 2017
| 