A168442 a(n) = 2^n * Product_{k=1..n} (4*k*(4*k+2))^(n-k).

1, 2, 96, 368640, 237817036800, 44185111712759808000, 3612115491258144161739571200000, 184260348281378257834400760180580024320000000

Offset: 0

Author

Paul Barry, Nov 25 2009

Keywords

• easy
• nonn

Comments

Hankel transform of A168441.

Crossrefs

Cf. A168441.

Programs

Mathematica

Table[2^n*Product[(4*k*(4*k+2))^(n-k), {k,1,n}], {n,0,10}] (* Vaclav Kotesovec, Jan 23 2024 *)

Formula

a(n) ~ Pi^(n/2) * 2^(2*n^2 + n + 5/24) * n^(n^2 + n/2 - 1/24) / (sqrt(A) * exp(3*n^2/2 + n/2 - 1/24)), where A is the Glaisher-Kinkelin constant A074962. - Vaclav Kotesovec, Jan 23 2024