A372240 a(n) = Product_{j=1..n} j^(floor(sqrt(j))).

1, 1, 2, 6, 96, 2400, 86400, 4233600, 270950400, 197522841600, 197522841600000, 262902902169600000, 454296214949068800000, 998088784243104153600000, 2738755623963077797478400000, 9243300230875387566489600000000, 605768923930649399557462425600000000

Offset: 0

Author

Vaclav Kotesovec, Apr 23 2024

Keywords

• nonn

Links

• Vaclav Kotesovec, Graph - the asymptotic ratio of log(a(n)) and log(A372241(n))

Crossrefs

Cf. A255322, A372241.

Programs

Mathematica

Table[Product[j^(Floor[Sqrt[j]]), {j, 1, n}], {n, 0, 17}]

Formula

a(n^2) = A372241(n^2) * n!^2 / (n^2)!.

a(n^2) = (n^2)!^n * n!^2 / A255322(n).

log(a(n)) ~ (2*n^(3/2)/3 - n/2 - 5*sqrt(n)/6 + 1/4)*log(n) - 4*n^(3/2)/9 + n/2 - sqrt(n).