A364400 G.f. satisfies A(x) = 1 + x/A(x)^3*(1 + 1/A(x)^3).

1, 2, -18, 270, -4902, 98538, -2110794, 47227846, -1090742094, 25806364434, -622267199554, 15236456140542, -377814588773622, 9468373002766074, -239434464005544570, 6101951612867546166, -156561081975745809566, 4040863076496835880226

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

G.f.: A(x) = 1/B(-x) where B(x) is the g.f. of A363304.

a(n) = (-1)^(n-1) * (1/n) * Sum_{k=0..n} binomial(n,k) * binomial(4*n+3*k-2,n-1) for n > 0.

a(n) ~ c*(-1)^(n+1)*256^n*27^(-n)*4F3([-n, 4*n/3, (4n-1)/3, (4*n+1)/3], [n, n+1/3, n+2/3], -1)*n^(-3/2), with c = (1/8)*sqrt (3/(2*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(4*n+3*k-2, n-1))/n);

Crossrefs

Cf. A364398, A364399.

Cf. A363304.

Sequence in context: A138275 A292693 A351275 * A334242 A349314 A365555

Adjacent sequences: A364397 A364398 A364399 * A364401 A364402 A364403

Keyword

sign

Author

Seiichi Manyama, Jul 22 2023

Status

approved