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A163086 Product of first n terms of A163085.

%I A163086 #15 Jul 11 2019 02:57:28
%S A163086 1,1,2,24,1728,3732480,161243136000,975198486528000000,
%T A163086 412860031256494080000000000,110116706384632080236544000000000000000,
%U A163086 7401233839469056679744633202278400000000000000000000
%N A163086 Product of first n terms of A163085.
%F A163086 a(n) = product_{i=0..n}  A056040(i+1)^(n-i). - _Peter Luschny_, Sep 18 2012
%p A163086 a := proc(n) local i; mul(A163085(i),i=0..n) end;
%t A163086 b[0] = 1; b[n_] := b[n] = b[n-1] n! / Floor[n/2]!^2;
%t A163086 a[n_] := Product[b[k], {k, 0, n}];
%t A163086 Table[a[n], {n, 0, 10}] (* _Jean-François Alcover_, Jul 11 2019 *)
%o A163086 (Sage)
%o A163086 def A163086(n):
%o A163086     swing = lambda n: factorial(n)/factorial(n//2)^2
%o A163086     return mul(swing(i+1)^(n-i) for i in (0..n))
%o A163086 [A163086(i) for i in (0..10)] # _Peter Luschny_, Sep 18 2012
%Y A163086 Cf. A056040, A163085, A055462, A000178.
%K A163086 nonn
%O A163086 0,3
%A A163086 _Peter Luschny_, Jul 21 2009