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Product of first n terms of A163085.
2

%I #15 Jul 11 2019 02:57:28

%S 1,1,2,24,1728,3732480,161243136000,975198486528000000,

%T 412860031256494080000000000,110116706384632080236544000000000000000,

%U 7401233839469056679744633202278400000000000000000000

%N Product of first n terms of A163085.

%F a(n) = product_{i=0..n} A056040(i+1)^(n-i). - _Peter Luschny_, Sep 18 2012

%p a := proc(n) local i; mul(A163085(i),i=0..n) end;

%t b[0] = 1; b[n_] := b[n] = b[n-1] n! / Floor[n/2]!^2;

%t a[n_] := Product[b[k], {k, 0, n}];

%t Table[a[n], {n, 0, 10}] (* _Jean-François Alcover_, Jul 11 2019 *)

%o (Sage)

%o def A163086(n):

%o swing = lambda n: factorial(n)/factorial(n//2)^2

%o return mul(swing(i+1)^(n-i) for i in (0..n))

%o [A163086(i) for i in (0..10)] # _Peter Luschny_, Sep 18 2012

%Y Cf. A056040, A163085, A055462, A000178.

%K nonn

%O 0,3

%A _Peter Luschny_, Jul 21 2009