A372241 a(n) = Product_{j=1..n} j^(ceiling(sqrt(j))).

1, 1, 4, 36, 576, 72000, 15552000, 5334336000, 2731180032000, 1991030243328000, 19910302433280000000, 291506737925652480000000, 6044683717626329825280000000, 172642211659125606139822080000000, 6632223203096969285467405025280000000, 335756299656784070076787379404800000000000

Offset: 0

Author

Vaclav Kotesovec, Apr 23 2024

Keywords

• nonn

Links

• Vaclav Kotesovec, Graph - the asymptotic ratio (1000 terms)

Crossrefs

Cf. A255322, A372240.

Cf. A088021.

Programs

Mathematica

Table[Product[j^(Ceiling[Sqrt[j]]), {j, 1, n}], {n, 0, 15}]

Formula

a(n^2) = (n^2)!^(n+1) / A255322(n).

log(a(n)) ~ (2*n^(3/2)/3 + n/2 - sqrt(n)/6 + 1/4)*log(n) - 4*n^(3/2)/9 - n/2 + sqrt(n).

a(n^2) / A372240(n^2) = (n^2)! / n!^2 = A088021(n).