A373577 Expansion of e.g.f. exp(x * (1 + x^2)^(3/2)).

1, 1, 1, 10, 37, 136, 1261, 6616, 45865, 479872, 3206521, 31165696, 356045581, 3082798720, 37528974757, 443190912256, 4792765859281, 69943918698496, 875123733523825, 11059833224507392, 179428023035501941, 2557848382674927616, 37699048392962570461

Offset

0,4

Links

Table of n, a(n) for n=0..22.

Formula

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

a(n) == 1 mod 9.

Prog

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

Crossrefs

Cf. A118395, A190863, A373578.

Sequence in context: A048480 A116970 A355044 * A199208 A110528 A208674

Adjacent sequences: A373574 A373575 A373576 * A373578 A373579 A373580

Keyword

nonn

Author

Seiichi Manyama, Jun 10 2024

Status

approved