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A294158 Row sums of A291844. 2
1, 1, 6, 52, 602, 8223, 128917, 2273716, 44509914, 957408649, 22449011336, 570032756328, 15587503694363, 456793916757139, 14284890417759141, 474896318288651220, 16726743380843538668, 622282429409944248297, 24385251974172090147514, 1004017088910699487855180 (list; graph; refs; listen; history; text; internal format)
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: A075756 A217486 A144345 * A209306 A271802 A097820

Adjacent sequences:  A294155 A294156 A294157 * A294159 A294160 A294161

KEYWORD

nonn

AUTHOR

Gheorghe Coserea, Oct 24 2017

STATUS

approved

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Last modified July 25 03:53 EDT 2021. Contains 346283 sequences. (Running on oeis4.)