A355268 a(n) = n! * [x^n] -exp(x^2)/(x - 1).

1, 1, 4, 12, 60, 300, 1920, 13440, 109200, 982800, 9858240, 108440640, 1301952960, 16925388480, 236972736000, 3554591040000, 56873975558400, 966857584492800, 17403454164096000, 330665629117824000, 6613313252799052800, 138879578308780108800, 3055350750951750451200

Offset: 0

Author

Peter Luschny, Jul 15 2022

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..449

Crossrefs

Cf. A000522.

Programs

Maple

egf := -exp(x^2)/(x - 1): ser := series(egf, x, 26):
seq(n!*coeff(ser, x, n), n = 0..22);

PARI

a(n) = n!*sum(k=0, n\2, 1/k!); \\ Seiichi Manyama, Jul 17 2022

Formula

a(n) = n!*hypergeom([-floor(n/2)], [-floor(n/2)], 1).

a(n) = n!*Sum_{k=0..floor(n/2)} 1/k!. - Seiichi Manyama, Jul 17 2022

D-finite with recurrence a(n) -n*a(n-1) +2*(-n+1)*a(n-2) +2*(n-1)*(n-2)*a(n-3)=0. - R. J. Mathar, Jul 27 2022

a(n) ~ exp(1) * n!. - Vaclav Kotesovec, Feb 28 2024