A373740 Expansion of e.g.f. exp(x^2/2 * (1 + x)).

1, 0, 1, 3, 3, 30, 105, 315, 2625, 11340, 57645, 467775, 2505195, 17027010, 142026885, 922296375, 7493911425, 65886420600, 503693415225, 4625660914875, 43369908657075, 379618464975750, 3824934458169825, 38406952928819475, 376103907454500225

Offset

0,4

Links

Table of n, a(n) for n=0..24.

Formula

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

a(n) = (n-1)/2 * (2*a(n-2) + 3*(n-2)*a(n-3)).

Prog

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

Crossrefs

Cf. A361567, A373741.

Cf. A182097.

Sequence in context: A151480 A096351 A367890 * A344934 A086667 A067098

Adjacent sequences: A373736 A373737 A373739 * A373741 A373742 A373743

Keyword

nonn

Author

Seiichi Manyama, Jun 16 2024

Status

approved