A373542 Expansion of e.g.f. exp(x * sqrt(1-x^2)).

1, 1, 1, -2, -11, -44, -59, -104, 1513, -4976, 14761, -1005344, -594659, -120135872, -8409491, -19661062784, 461914321, -4406419844864, 8555830993, -1268264427577856, -595229416379, -455779307821067264, -13631036685419, -200172063313066452992

Offset

0,4

Links

Table of n, a(n) for n=0..23.

Formula

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

a(n) == 1 mod 3.

Prog

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

Crossrefs

Cf. A190863.

Sequence in context: A241712 A066058 A153440 * A289645 A181369 A037744

Adjacent sequences: A373539 A373540 A373541 * A373543 A373544 A373545

Keyword

sign

Author

Seiichi Manyama, Jun 09 2024

Status

approved