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%I #17 Mar 08 2022 14:17:24
%S 1,2,10,82,898,12018,187626,3323682,65607682,1424967394,33736908874,
%T 864372576626,23825543471234,703074672632018,22118247888976170,
%U 739081808704195650,26146116129400483842,976382058777174451650,38386296866727499728522,1584986693941237056394386
%N Row sums of A286796.
%H Gheorghe Coserea, <a href="/A286797/b286797.txt">Table of n, a(n) for n = 0..200</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..n} A286796(n,k).
%F a(n) ~ 2^(n + 5/2) * n^(n+2) / exp(n+2). - _Vaclav Kotesovec_, Mar 08 2022
%t max = 20; y0[x_, t_] = 1; y1[x_, t_] = 0; For[n = 1, n <= max, n++, y1[x_, t_] = (1 + x*(1 + 2*t + x*t^2)*y0[x, t]^2 + t*(1 - t)*x^2*y0[x, t]^3 + 2*x^2*y0[x, t]*D[y0[x, t], x])/(1 + 2*x*t) + O[x]^n // Normal // Simplify; y0[x_, t_] = y1[x, t]];
%t a[n_] := CoefficientList[SeriesCoefficient[y0[x, t]/(1 - x*t*y0[x, t]), {x, 0, n}], t] // Total;
%t Table[a[n], {n, 0, max-1}] (* _Jean-François Alcover_, May 24 2017, adapted from PARI *)
%o (PARI)
%o A286795_ser(N, t='t) = {
%o my(x='x+O('x^N), y0=1, y1=0, n=1);
%o while(n++,
%o y1 = (1 + x*(1 + 2*t + x*t^2)*y0^2 + t*(1-t)*x^2*y0^3 + 2*x^2*y0*y0');
%o y1 = y1 / (1+2*x*t); if (y1 == y0, break()); y0 = y1;); y0;
%o };
%o A286796_ser(N,t='t) = my(v=A286795_ser(N,t)); v/(1-x*t*v);
%o Vec(A286796_ser(20,1))
%o (PARI)
%o A049464_ser(N) = { \\ for A049464(0)=0
%o my(s=Ser(concat(1, vector(N+1, n, (2*n)!/(2^n*n!)))), g=(1/s - 1/s^2)/x);
%o 1 - 1/subst(g, 'x, serreverse(x*g^2*s^2));
%o };
%o A286797_ser(N) = my(q=A049464_ser(N)); q/(x-x*q);
%o Vec(A286797_ser(20))
%Y Cf. A286796.
%K nonn
%O 0,2
%A _Gheorghe Coserea_, May 21 2017
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