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a(n) = |Stirling1(n, floor(n/2))| * floor(n/2)!.
1

%I #11 Aug 27 2022 17:13:18

%S 1,0,1,2,22,100,1350,9744,162456,1614816,32319000,410031600,

%T 9604465200,148370508000,3986353491120,72622987557120,

%U 2202727143576960,46243059751848960,1563325251963995520,37165349757066935040,1385918755006365216000,36804377751967949760000

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

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

%p a := n -> abs(Stirling1(n, floor(n/2))) * floor(n/2)! :

%p seq(a(n), n = 0..21);

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

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

%K nonn

%O 0,4

%A _Peter Luschny_, May 22 2021