A358499 a(n) = Sum_{k=0..floor(n/4)} (n-4*k)!.
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
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..449
Programs
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PARI
a(n) = sum(k=0, n\4, (n-4*k)!);
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