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a(n) = n! * Sum_{j=0..floor(n/2)} (-1)^j/binomial(n,j).
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%I #20 Jul 13 2019 10:46:39

%S 1,1,1,4,22,108,612,4416,36576,331200,3319200,36806400,445046400,

%T 5813579520,81716947200,1230656716800,19761225523200,336973967769600,

%U 6082189179494400,115851849523200000,2322322137354240000,48869666136023040000

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

%p a:= n-> n!*add((-1)^j/binomial(n, j), j=0..iquo(n, 2)):

%p seq(a(n), n=0..23); # _Alois P. Heinz_, Jul 10 2019

%t Table[n!*Sum[(-1)^k/Binomial[n, k], {k, 0, Floor[n/2]}], {n, 0, 20}] (* _Vaclav Kotesovec_, Jul 10 2019 *)

%K nonn

%O 0,4

%A _Clark Kimberling_

%E More terms from _Sean A. Irvine_, Jul 10 2019