A286799 - OEIS

%I #10 May 26 2017 22:18:32

%S 1,1,6,49,542,7278,113824,2017881,39842934,865391422,20486717908,

%T 524816312106,14463876594476,426759508580416,13423937511765492,

%U 448515527244396873,15865571912065180326,592432249691301719190,23290086526099237126180,961614574423928988516286,41607005553456012247259844

%N Row sums of A286798.

%H Gheorghe Coserea, <a href="/A286799/b286799.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.

%t max = 22; y0[x_, t_] = 1; y1[x_, t_] = 0; For[n = 1, n <= max, n++, y1[x_, t_] = 1 + x y0[x, t]^2 + 3 t x^3 y0[x, t]^2 D[y0[x, t], x] + x^2 (2 y0[x, t] D[y0[x, t], x] + t (2 y0[x, t]^3 - D[y0[x, t], x] + y0[x, t] D[y0[x, t], x])) + O[x]^n // Normal // Simplify; y0[x_, t_] = y1[x, t]];

%t P[n_, t_] := Coefficient[y0[x, t] , x, n];

%t a[n_] := CoefficientList[P[n, t], 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 A286798_ser(N,t='t) = {

%o   my(v = A286795_ser(N,t)); subst(v, 'x, serreverse(x/(1-x*t*v)));

%o };

%o Vec(A286798_ser(21,1))

%Y Cf. A286798.

%K nonn

%O 0,3

%A _Gheorghe Coserea_, May 21 2017