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