A372150 a(n) = Product_{k=1..n} k!^(k^2).

1, 1, 16, 161243136, 1953714516870533385423459188736, 18637697331204402735774894643901575833450808531469488619520000000000000000000000000

Offset: 0

Author

Vaclav Kotesovec, Apr 20 2024

Keywords

• nonn

Crossrefs

Cf. A051675, A255269.

Programs

Mathematica

Table[Product[k!^(k^2), {k, 1, n}], {n, 0, 6}]

Formula

a(n) ~ (2*Pi)^(n^3/6 + n^2/4 + n/12) * n^(n^4/4 + 2*n^3/3 + n^2/2 + n/12 - 1/90) / (A^(1/6) * exp(5*n^4/16 + 5*n^3/9 + n^2/8 - n/12 - zeta(3)/(8*Pi^2) - zeta'(-3)/3 - 13/720)), where A is the Glaisher-Kinkelin constant A074962, zeta(3) = A002117, zeta'(-3) = A259068.