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%I #7 Jan 23 2024 11:27:51
%S 1,2,96,368640,237817036800,44185111712759808000,
%T 3612115491258144161739571200000,
%U 184260348281378257834400760180580024320000000
%N a(n) = 2^n * Product_{k=1..n} (4*k*(4*k+2))^(n-k).
%C Hankel transform of A168441.
%F 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
%t Table[2^n*Product[(4*k*(4*k+2))^(n-k), {k,1,n}], {n,0,10}] (* _Vaclav Kotesovec_, Jan 23 2024 *)
%Y Cf. A168441.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Nov 25 2009
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