A373668 Expansion of e.g.f. exp(x / (1 - x^2)^3).

1, 1, 1, 19, 73, 901, 7921, 88831, 1261009, 15786793, 284515201, 4359416491, 88359404761, 1671036171949, 36734936604913, 831051144091351, 19848996799904161, 516144198653004241, 13522792578340917889, 391107276466207593283, 11295497154349628317801

Offset

0,4

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = n! * Sum_{k=0..floor(n/2)} binomial(3*n-5*k-1,k)/(n-2*k)!.

a(n) == 1 (mod 18).

Prog

(PARI) a(n) = n!*sum(k=0, n\2, binomial(3*n-5*k-1, k)/(n-2*k)!);

Crossrefs

Cf. A012150, A088009, A373619, A373620, A373667.

Cf. A373653, A373682.

Sequence in context: A373720 A118593 A047979 * A290241 A159997 A073566

Adjacent sequences: A373665 A373666 A373667 * A373669 A373670 A373671

Keyword

nonn

Author

Seiichi Manyama, Jun 13 2024

Status

approved