A364397 G.f. satisfies A(x) = 1 + x/A(x)^2*(1 + 1/A(x)^2).

1, 2, -12, 124, -1560, 21776, -324256, 5046096, -81086112, 1335113408, -22408067200, 381942129792, -6593494698752, 115044039049728, -2025580621035520, 35943759448886528, -642162301086308864, 11541259115333684224, -208521418711421405184

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Formula

G.f.: A(x) = 1/B(-x) where B(x) is the g.f. of A363311.

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

a(n) ~ c*(-1)^(n+1)*27^n*4^(-n)*3F2([-n, 3*n/2, (3n-1)/2], [n, n+1/2], -1)*n^(-3/2), with c = 1/(3*sqrt(3*Pi)). - Stefano Spezia, Oct 21 2023

Prog

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

Crossrefs

Cf. A364393, A364395, A364399.

Cf. A363311.

Sequence in context: A372178 A246738 A039933 * A214223 A173219 A227458

Adjacent sequences: A364394 A364395 A364396 * A364398 A364399 A364400

Keyword

sign

Author

Seiichi Manyama, Jul 22 2023

Status

approved