%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