A373538 Expansion of e.g.f. exp(x/(1 + x^2)).

1, 1, 1, -5, -23, 61, 961, -209, -64175, -197063, 6153121, 48453571, -775290119, -12038136395, 116706067297, 3475641927031, -17614393396319, -1188106176788879, 782498662651585, 478042340115562507, 1987706898622853641, -223468834844001403859

Offset: 0

Author

Seiichi Manyama, Jun 09 2024

Keywords

• sign

Crossrefs

Cf. A012019.

Programs

PARI

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

Formula

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

a(n) == 1 mod 6.