A358607 a(n) = Sum_{k=0..floor(n/2)} (-1)^k * (n-2*k)!.

1, 1, 1, 5, 23, 115, 697, 4925, 39623, 357955, 3589177, 39558845, 475412423, 6187461955, 86702878777, 1301486906045, 20836087009223, 354385941189955, 6381537618718777, 121290714467642045, 2426520470557921223, 50969651457241797955, 1121574207307049758777

Offset: 0

Author

Seiichi Manyama, Nov 23 2022

Keywords

• nonn

Links

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

Crossrefs

Cf. A358608, A358609, A358611.

Cf. A121868, A136580.

Programs

PARI

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

Formula

a(n) = n * a(n-1) - a(n-2) + n * a(n-3) for n > 2.

a(n) ~ n! * (1 - 1/n^2 - 1/n^3 + 5/n^5 + 23/n^6 + 74/n^7 + 161/n^8 - 57/n^9 - 3466/n^10 - ...), for coefficients see A121868. - Vaclav Kotesovec, Nov 25 2022

a(2n) = 1+A215096(2n). a(2n+1) = A215096(2n+1). - R. J. Mathar, Jun 14 2024