A168440 - OEIS

%I #7 Jan 23 2024 11:20:19

%S 1,3,315,3274425,6637341335625,4345660353133020796875,

%T 1374246178519871776155872382421875,

%U 293343904920011883594420118662644304008056640625

%N a(n) = Product_{k=0..n} ((4*k+1)*(4*k+3))^(n-k).

%C Hankel transform of A128709.

%F a(n) ~ A^(1/4) * sqrt(Gamma(1/4)) * 2^(2*n^2 + 5*n/2 + 1/8) * n^(n^2 + n + 7/48) / (Pi^(1/4) * exp(3*n^2/2 + n + 1/48)), where A is the Glaisher-Kinkelin constant A074962. - _Vaclav Kotesovec_, Jan 23 2024

%t Table[Product[((4*k+1)*(4*k+3))^(n-k), {k,0,n}], {n,0,10}] (* _Vaclav Kotesovec_, Jan 23 2024 *)

%Y Cf. A128709.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Nov 25 2009