A368623 - OEIS

%I #7 Jan 06 2024 15:06:56

%S 1,3,108,11286,2337984,804305700,414285404544,298436020283016,

%T 286455044544970752,353358684943164351792,544692796454778554880000,

%U 1025983872949208210500475232,2318663822077115453077590638592,6191980828123077577798830642106944,19289639610614384872295428226588737536

%N a(n) = Product_{k=1..n} (k^2 + 2*n^2).

%C In general, for d>0, Product_{k=1..n} (k^2 + d*n^2) ~ (d+1)^(n + 1/2) * exp(n*(sqrt(d)*(Pi - 2*arctan(sqrt(d))) - 2)) * n^(2*n) / sqrt(d). - _Vaclav Kotesovec_, Jan 06 2024

%F a(n) ~ 3^(n + 1/2) * exp(n*(sqrt(2)*arctan(2*sqrt(2)) - 2)) * n^(2*n) / sqrt(2).

%t Table[Product[k^2 + 2*n^2, {k, 1, n}], {n, 0, 20}]

%Y Cf. A272244, A324403, A324425.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Jan 01 2024