A364396 G.f. satisfies A(x) = 1 + x/A(x)^2*(1 + 1/A(x)).

1, 2, -10, 86, -902, 10506, -130594, 1697006, -22774094, 313205522, -4391039930, 62522730310, -901680559574, 13143551082138, -193339856081490, 2866341942620382, -42784807130635678, 642457682754511906, -9698259831536382826, 147091417979841002294

Offset: 0

Author

Seiichi Manyama, Jul 22 2023

Keywords

• sign

Crossrefs

Cf. A112478, A364394, A364398.

Cf. A144097.

Programs

PARI

a(n) = if(n==0, 1, (-1)^(n-1)*sum(k=0, n, binomial(n, k)*binomial(3*n+k-2, n-1))/n);

Formula

G.f.: A(x) = 1/B(-x) where B(x) is the g.f. of A144097.

a(n) = (-1)^(n-1) * (1/n) * Sum_{k=0..n} binomial(n,k) * binomial(3*n+k-2,n-1) for n > 0.

a(n) ~ c*(-1)^(n+1)*4^(-n)*27^n*n^(-3/2)*2F1([-n, 3*n-1], [2*n], -1), with c = 1/(3*sqrt(3*Pi)). - Stefano Spezia, Oct 21 2023