A358499 - OEIS

%I #14 Nov 24 2022 04:22:10

%S 1,1,2,6,25,121,722,5046,40345,363001,3629522,39921846,479041945,

%T 6227383801,87181920722,1307714289846,20923268929945,355693655479801,

%U 6402460887648722,121646408123121846,2432922931445569945,51091297865364919801,1124007130238495328722

%N a(n) = Sum_{k=0..floor(n/4)} (n-4*k)!.

%H Seiichi Manyama, <a href="/A358499/b358499.txt">Table of n, a(n) for n = 0..449</a>

%F a(n) = n * a(n-1) + a(n-4) - n * a(n-5) for n > 4.

%F 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

%o (PARI) a(n) = sum(k=0, n\4, (n-4*k)!);

%Y Cf. A136580, A358498, A358500.

%K nonn,easy

%O 0,3

%A _Seiichi Manyama_, Nov 19 2022