A358500 - OEIS

%I #17 Nov 24 2022 04:48:47

%S 1,1,2,6,24,121,721,5042,40326,362904,3628921,39917521,479006642,

%T 6227061126,87178654104,1307677996921,20922829805521,355687907102642,

%U 6402379932789126,121645187587486104,2432903315854636921,51090963094539245521,1124001083465514782642

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

%H Seiichi Manyama, <a href="/A358500/b358500.txt">Table of n, a(n) for n = 0..449</a>

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

%F 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

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

%Y Cf. A136580, A358498, A358499.

%K nonn,easy

%O 0,3

%A _Seiichi Manyama_, Nov 19 2022