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
KEYWORD
nonn
AUTHOR
Gheorghe Coserea, Oct 24 2017
STATUS
approved