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

0,3

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.

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 *)

Prog

(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))

Crossrefs

Cf. A286798.

Sequence in context: A143165 A008786 A274278 * A245797 A046195 A305376

Adjacent sequences: A286796 A286797 A286798 * A286800 A286801 A286802

Keyword

nonn

Author

Gheorghe Coserea, May 21 2017

Status

approved