A358603 a(n) = Sum_{k=0..floor(n/2)} (-1)^k * (n-k)!/(n-2*k)!.

1, 1, 0, -1, 0, 3, 2, -9, -12, 35, 78, -153, -544, 723, 4170, -3337, -35028, 10851, 320678, 57255, -3178152, -2190253, 33864546, 42120183, -385314460, -719159517, 4649508222, 12033407591, -59076411312, -204022615725, 784134861818, 3554417974647, -10768948801764

Offset: 0

Author

Seiichi Manyama, Nov 23 2022

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..899

Crossrefs

Cf. A358604, A358605, A358606.

Cf. A122852.

Programs

Mathematica

nxt[{n_,a_,b_}]:={n+1,b,(b-a(n+1)+1)/2}; NestList[nxt,{1,1,1},40][[;;,2]] (* Harvey P. Dale, Jul 25 2024 *)

PARI

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

Formula

a(n) = (a(n-1) - n * a(n-2) + 1)/2 for n > 1.