A294158 Row sums of A291844.

1, 1, 6, 52, 602, 8223, 128917, 2273716, 44509914, 957408649, 22449011336, 570032756328, 15587503694363, 456793916757139, 14284890417759141, 474896318288651220, 16726743380843538668, 622282429409944248297, 24385251974172090147514, 1004017088910699487855180

Offset: 0

Author

Gheorghe Coserea, Oct 24 2017

Keywords

• nonn

Links

• Gheorghe Coserea, Table of n, a(n) for n = 0..202
• Luca G. Molinari, Nicola Manini, Enumeration of many-body skeleton diagrams, arXiv:cond-mat/0512342 [cond-mat.str-el], 2006.

Crossrefs

Cf. A049464(y), A287039(x), A286799(z), A287029(u), A291844.

Programs

PARI

A291843_ser(N, t='t) = {
  my(x='x+O('x^N), y=1, y1=0, n=1,
  dn = 1/(-2*t^2*x^4 - (2*t^2+3*t)*x^3 - (2*t+1)*x^2 + (2*t-1)*x + 1));
  while (n++,
   y1 = (2*x^2*y'*((-t^2 + t)*x + (-t + 1) + (t^2*x^2 + (t^2 + t)*x + t)*y) +
        (t*x^2 + t*x)*y^2 - (2*t^2*x^3 + 3*t*x^2 + (-t + 1)*x - 1))*dn;
   if (y1 == y, break); y = y1;); y;
};
A291844_ser(N, t='t) = {
  my(z = A291843_ser(N+1,t));
  ((1+x)*z - 1)*(1 + t*x)/((1-t + t*(1+x)*z)*x*z^2);
};
Vec(A291844_ser(20,t=1))

Formula

a(n) = Sum_{k=0..floor((2*n-1)/3)} A291844(n,k), n > 0.