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A373538
Expansion of e.g.f. exp(x/(1 + x^2)).
0
1, 1, 1, -5, -23, 61, 961, -209, -64175, -197063, 6153121, 48453571, -775290119, -12038136395, 116706067297, 3475641927031, -17614393396319, -1188106176788879, 782498662651585, 478042340115562507, 1987706898622853641, -223468834844001403859
OFFSET
0,4
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.
PROG
(PARI) a(n) = n!*sum(k=0, n\2, (-1)^k*binomial(n-k-1, k)/(n-2*k)!);
CROSSREFS
Cf. A012019.
Sequence in context: A098498 A159241 A179094 * A176874 A331987 A241765
KEYWORD
sign
AUTHOR
Seiichi Manyama, Jun 09 2024
STATUS
approved