A168440 a(n) = Product_{k=0..n} ((4*k+1)*(4*k+3))^(n-k).

1, 3, 315, 3274425, 6637341335625, 4345660353133020796875, 1374246178519871776155872382421875, 293343904920011883594420118662644304008056640625

Offset: 0

Author

Paul Barry, Nov 25 2009

Keywords

• easy
• nonn

Comments

Hankel transform of A128709.

Crossrefs

Cf. A128709.

Programs

Mathematica

Table[Product[((4*k+1)*(4*k+3))^(n-k), {k,0,n}], {n,0,10}] (* Vaclav Kotesovec, Jan 23 2024 *)

Formula

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