A367927 a(n) = Product_{k=1..n} (n^2 + k^2)^k.

1, 2, 320, 9856080, 111411200000000, 758912215744345000000000, 4641055652546245989752776320614400000, 35539706227151665491451514343890494014992000000000000, 453355203871266077337924186645041169745278527392553369600000000000000000

Offset: 0

Author

Vaclav Kotesovec, Dec 05 2023

Keywords

• nonn

Crossrefs

Cf. A272244.

Programs

Mathematica

Table[Product[(k^2 + n^2)^k, {k, 1, n}], {n, 0, 10}]

Formula

a(n) ~ 2^(n^2 + n/2 + 1/12) * n^(n*(n+1)) / exp(n^2/2 - 1/12).