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a(n) = Product_{k=0..n} (2*k^2)!.
1

%I #6 Mar 31 2024 07:51:02

%S 1,2,80640,516287415629905920000,

%T 135851139773030831011345707357554182190215987200000000000

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

%C The next term has 121 digits.

%F a(n) ~ c * 2^(2*n^3/3 + n^2 + 4*n/3) * Pi^(n/2) * n^(4*n^3/3 + 2*n^2 + 5*n/3 + 1/2) / exp(10*n^3/9 + n^2 + n), where c = 3.03114159524498232897099596239043047625469924617878376047699145874714076...

%t Table[Product[(2*k^2)!, {k, 0, n}], {n, 0, 6}]

%Y Cf. A255322.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Mar 31 2024