A358609 - OEIS

%I #15 Nov 25 2022 06:44:02

%S 1,1,2,6,23,119,718,5034,40297,362761,3628082,39911766,478961303,

%T 6226658039,87174663118,1307634456234,20922310926697,355681201437961,

%U 6402286531064882,121643792774375766,2432881085865713303,51090586490508002039,1123994325491076615118

%N a(n) = Sum_{k=0..floor(n/4)} (-1)^k * (n-4*k)!.

%H Seiichi Manyama, <a href="/A358609/b358609.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 - 300/n^8 - 938/n^9 - 2563/n^10 - ...). - _Vaclav Kotesovec_, Nov 25 2022

%o (PARI) a(n) = sum(k=0, n\4, (-1)^k*(n-4*k)!);

%Y Cf. A358607, A358608, A358611.

%Y Cf. A358499.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Nov 23 2022