A294321 - OEIS

%I #5 Oct 28 2017 11:05:00

%S 2,1440,5225472000,455547719673446400000,

%T 2916586742141623158009180979200000000,

%U 3278245620793706216637861108629164518335840256000000000000

%N a(n) = Product_{k=0..n} (4*k + 2)!.

%F a(n) ~ 2^(4*n^2 + 19*n/2 + 35/6) * n^(2*n^2 + 9*n/2 + 113/48) * Pi^(n/2 + 3/4) / (A^(1/4) * Gamma(1/4)^(1/2) * exp(3*n^2 + 9*n/2 - 1/48)), where A is the Glaisher-Kinkelin constant A074962.

%F A268505(n) * A294320(n) * A294321(n) * A294322(n) = A000178(4*n + 3).

%t Table[Product[(4*k + 2)!, {k, 0, n}] , {n, 0, 10}]

%Y Cf. A268505, A294319, A294320, A294322, A294324.

%K nonn

%O 0,1

%A _Vaclav Kotesovec_, Oct 28 2017