A358607 - OEIS

%I #17 Jun 14 2024 11:53:17

%S 1,1,1,5,23,115,697,4925,39623,357955,3589177,39558845,475412423,

%T 6187461955,86702878777,1301486906045,20836087009223,354385941189955,

%U 6381537618718777,121290714467642045,2426520470557921223,50969651457241797955,1121574207307049758777

%N a(n) = Sum_{k=0..floor(n/2)} (-1)^k * (n-2*k)!.

%H Seiichi Manyama, <a href="/A358607/b358607.txt">Table of n, a(n) for n = 0..449</a>

%F a(n) = n * a(n-1) - a(n-2) + n * a(n-3) for n > 2.

%F a(n) ~ n! * (1 - 1/n^2 - 1/n^3 + 5/n^5 + 23/n^6 + 74/n^7 + 161/n^8 - 57/n^9 - 3466/n^10 - ...), for coefficients see A121868. - _Vaclav Kotesovec_, Nov 25 2022

%F a(2n) = 1+A215096(2n). a(2n+1) = A215096(2n+1). - _R. J. Mathar_, Jun 14 2024

%o (PARI) a(n) = sum(k=0, n\2, (-1)^k*(n-2*k)!);

%Y Cf. A358608, A358609, A358611.

%Y Cf. A121868, A136580.

%K nonn

%O 0,4

%A _Seiichi Manyama_, Nov 23 2022