A373619 Expansion of e.g.f. exp(x / (1 - x^2)^(3/2)).

1, 1, 1, 10, 37, 316, 2341, 21736, 237385, 2611792, 35911081, 476570656, 7654975021, 121021831360, 2196593121997, 40464132512896, 817485662059921, 17159299818547456, 382733978898335185, 8982388245979044352, 219867829220866999861, 5684505550914409716736

Offset

0,4

Links

Table of n, a(n) for n=0..21.

Formula

a(n) = n! * Sum_{k=0..floor(n/2)} binomial(3*n/2-2*k-1,k)/(n-2*k)!.

a(n) == 1 mod 9.

a(n) ~ 3^(1/5) * 5^(-1/2) * exp(3^(-1/5)*n^(1/5)/4 + 5*3^(-3/5)*n^(3/5)/2 - n) * n^(n - 1/5) * (1 - 1/(10*3^(4/5)*n^(1/5))). - Vaclav Kotesovec, Jun 11 2024

Prog

(PARI) a(n) = n!*sum(k=0, n\2, binomial(3*n/2-2*k-1, k)/(n-2*k)!);

Crossrefs

Cf. A012150, A088009, A373620.

Cf. A373577.

Sequence in context: A208674 A137280 A071261 * A129426 A215881 A279543

Adjacent sequences: A373616 A373617 A373618 * A373620 A373621 A373622

Keyword

nonn

Author

Seiichi Manyama, Jun 11 2024

Status

approved