A286799 Row sums of A286798.

1, 1, 6, 49, 542, 7278, 113824, 2017881, 39842934, 865391422, 20486717908, 524816312106, 14463876594476, 426759508580416, 13423937511765492, 448515527244396873, 15865571912065180326, 592432249691301719190, 23290086526099237126180, 961614574423928988516286, 41607005553456012247259844

Offset: 0

Author

Gheorghe Coserea, May 21 2017

Keywords

• nonn

Links

• Gheorghe Coserea, Table of n, a(n) for n = 0..200
• Luca G. Molinari, Nicola Manini, Enumeration of many-body skeleton diagrams, arXiv:cond-mat/0512342 [cond-mat.str-el], 2006.

Crossrefs

Cf. A286798.

Programs

Mathematica

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]];
P[n_, t_] := Coefficient[y0[x, t] , x, n];
a[n_] := CoefficientList[P[n, t], t] // Total;
Table[a[n], {n, 0, max-1}] (* Jean-François Alcover, May 24 2017, adapted from PARI *)

PARI

A286795_ser(N, t='t) = {
  my(x='x+O('x^N), y0=1, y1=0, n=1);
  while(n++,
    y1 = (1 + x*(1 + 2*t + x*t^2)*y0^2 + t*(1-t)*x^2*y0^3 + 2*x^2*y0*y0');
    y1 = y1 / (1+2*x*t); if (y1 == y0, break()); y0 = y1;); y0;
};
A286798_ser(N,t='t) = {
  my(v = A286795_ser(N,t)); subst(v, 'x, serreverse(x/(1-x*t*v)));
};
Vec(A286798_ser(21,1))