A344498 a(n) = |Stirling1(n, floor(n/2))| * floor(n/2)!.

1, 0, 1, 2, 22, 100, 1350, 9744, 162456, 1614816, 32319000, 410031600, 9604465200, 148370508000, 3986353491120, 72622987557120, 2202727143576960, 46243059751848960, 1563325251963995520, 37165349757066935040, 1385918755006365216000, 36804377751967949760000

Offset: 0

Author

Peter Luschny, May 22 2021

Keywords

• nonn

Crossrefs

Cf. A132393, A225479 (middle column), A344397.

Programs

Maple

a := n -> abs(Stirling1(n, floor(n/2))) * floor(n/2)! :
seq(a(n), n = 0..21);

Mathematica

a[n_] := Abs @ StirlingS1[n, Floor[n/2]] * Floor[n/2]!; Array[a, 22, 0] (* Amiram Eldar, May 22 2021 *)

Formula

a(n) = floor(n/2)! * [x^floor(n/2)] Pochhammer(x, n).