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a(n) = ((2n+1)!)^2.
13

%I #16 Nov 20 2024 16:13:53

%S 1,36,14400,25401600,131681894400,1593350922240000,

%T 38775788043632640000,1710012252724199424000000,

%U 126513546505547170185216000000,14797530453474819213543604224000000

%N a(n) = ((2n+1)!)^2.

%F a(n) = A009445(n)^2 = A001044(2n+1). - _Wesley Ivan Hurt_, May 02 2014

%F From _Amiram Eldar_, Nov 16 2020: (Start)

%F Sum_{n>=0} 1/a(n) = A334378.

%F Sum_{n>=0} (-1)^n/a(n) = Im(BesselJ(0, 2*exp(3*Pi*i/4))). (End)

%p A134374:=n->((2*n+1)!)^2; seq(A134374(n), n=0..10); # _Wesley Ivan Hurt_, May 02 2014

%t Table[((2n+1)!)^(2), {n, 0, 10}]

%o (PARI) a(n) = ((2*n+1)!)^2; \\ _Michel Marcus_, Nov 16 2020

%Y Cf. A000142, A001044, A000442, A036740, A010050, A009445, A134366, A134367, A134368, A134369, A134371, A134372, A134373, A134375, A334378.

%K nonn,easy

%O 0,2

%A _Artur Jasinski_, Oct 22 2007