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URL: https://oeis.org/A358499

⇱ A358499 - OEIS

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A358499
a(n) = Sum_{k=0..floor(n/4)} (n-4*k)!.
6
1, 1, 2, 6, 25, 121, 722, 5046, 40345, 363001, 3629522, 39921846, 479041945, 6227383801, 87181920722, 1307714289846, 20923268929945, 355693655479801, 6402460887648722, 121646408123121846, 2432922931445569945, 51091297865364919801, 1124007130238495328722
OFFSET
0,3
LINKS
FORMULA
a(n) = n * a(n-1) + a(n-4) - n * a(n-5) for n > 4.
a(n) ~ n! * (1 + 1/n^4 + 6/n^5 + 25/n^6 + 90/n^7 + 302/n^8 + 994/n^9 + 3487/n^10 + ...), for coefficients see A099948. - Vaclav Kotesovec, Nov 24 2022
MATHEMATICA
Table[Sum[(n-4k)!, {k, 0, Floor[n/4]}], {n, 0, 30}] (* Harvey P. Dale, Feb 22 2026 *)
PROG
(PARI) a(n) = sum(k=0, n\4, (n-4*k)!);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Nov 19 2022
STATUS
approved