A373683 Expansion of e.g.f. exp(x / (1 - x^2)) / (1 - x^2).

1, 1, 3, 13, 61, 441, 3031, 28813, 267513, 3088081, 36278731, 491262861, 6962025973, 108395586313, 1791145742751, 31601369155021, 594291393830641, 11740929829286433, 246910933786777363, 5406641472165854221, 125497950720670828461, 3018786042678264770521

Offset

0,3

Links

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

Formula

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

a(n) == 1 (mod 2).

Prog

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

Crossrefs

Cf. A373681, A373682.

Cf. A088009.

Sequence in context: A375651 A246689 A355987 * A141786 A122122 A093424

Adjacent sequences: A373680 A373681 A373682 * A373684 A373685 A373686

Keyword

nonn

Author

Seiichi Manyama, Jun 13 2024

Status

approved