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

0,3

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.

Formula

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

Prog

(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))

Crossrefs

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

Sequence in context: A363008 A217486 A144345 * A209306 A271802 A097820

Adjacent sequences: A294155 A294156 A294157 * A294159 A294160 A294161

Keyword

nonn

Author

Gheorghe Coserea, Oct 24 2017

Status

approved