A358608 a(n) = Sum_{k=0..floor(n/3)} (-1)^k * (n-3*k)!.

1, 1, 2, 5, 23, 118, 715, 5017, 40202, 362165, 3623783, 39876598, 478639435, 6223397017, 87138414602, 1307195728565, 20916566490983, 355600289681398, 6401066509999435, 121624183842341017, 2432546407886958602, 51084541105199440565, 1123879103593765338983

Offset

0,3

Links

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

Formula

a(n) = n * a(n-1) - a(n-3) + n * a(n-4) for n > 3.

a(n) ~ n! * (1 - 1/n^3 - 3/n^4 - 7/n^5 - 14/n^6 - 16/n^7 + 77/n^8 + 922/n^9 + 6660/n^10 + ...), for coefficients see A143630. - Vaclav Kotesovec, Nov 25 2022

Prog

(PARI) a(n) = sum(k=0, n\3, (-1)^k*(n-3*k)!);

Crossrefs

Cf. A358607, A358609, A358611.

Cf. A143630, A358498.

Sequence in context: A003501 A006990 A378335 * A242227 A032182 A165902

Adjacent sequences: A358605 A358606 A358607 * A358609 A358610 A358611

Keyword

nonn

Author

Seiichi Manyama, Nov 23 2022

Status

approved