A358500 a(n) = Sum_{k=0..floor(n/5)} (n-5*k)!.

1, 1, 2, 6, 24, 121, 721, 5042, 40326, 362904, 3628921, 39917521, 479006642, 6227061126, 87178654104, 1307677996921, 20922829805521, 355687907102642, 6402379932789126, 121645187587486104, 2432903315854636921, 51090963094539245521, 1124001083465514782642

Offset

0,3

Links

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

Formula

a(n) = n * a(n-1) + a(n-5) - n * a(n-6) for n > 5.

a(n) ~ n! * (1 + 1/n^5 + 10/n^6 + 65/n^7 + 350/n^8 + 1701/n^9 + 7771/n^10 + 34150/n^11 + 146905/n^12 + ...), the coefficients are Sum_{j=0..(k-4)/5} Stirling2(k,5*j+4). - Vaclav Kotesovec, Nov 24 2022

Prog

(PARI) a(n) = sum(k=0, n\5, (n-5*k)!);

Crossrefs

Cf. A136580, A358498, A358499.

Sequence in context: A114779 A317681 A230363 * A358494 A357922 A275753

Adjacent sequences: A358497 A358498 A358499 * A358501 A358502 A358503

Keyword

nonn,easy

Author

Seiichi Manyama, Nov 19 2022

Status

approved