A364399 G.f. satisfies A(x) = 1 + x/A(x)^3*(1 + 1/A(x)^2).

1, 2, -16, 212, -3400, 60384, -1142960, 22598832, -461250208, 9644611008, -205537131008, 4447969973888, -97482797466624, 2159242220999936, -48260706692535552, 1087076798266594048, -24652590023639251456, 562396337623786449920

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 A363380.

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

a(n) ~ c*(-1)^(n-1)*256^n*27^(-n)*3F2([-n, 2*n, 2*n-1/2], [3*n/2, (3*n+1)/2], -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+2*k-2, n-1))/n);

Crossrefs

Cf. A364393, A364395, A364397.

Cf. A364398, A364400.

Cf. A363380.

Sequence in context: A206930 A206865 A349313 * A365568 A360939 A114531

Adjacent sequences: A364396 A364397 A364398 * A364400 A364401 A364402

Keyword

sign

Author

Seiichi Manyama, Jul 22 2023

Status

approved