A372241 - OEIS

%I #9 Apr 23 2024 15:17:04

%S 1,1,4,36,576,72000,15552000,5334336000,2731180032000,

%T 1991030243328000,19910302433280000000,291506737925652480000000,

%U 6044683717626329825280000000,172642211659125606139822080000000,6632223203096969285467405025280000000,335756299656784070076787379404800000000000

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

%H Vaclav Kotesovec, <a href="/A372241/a372241.jpg">Graph - the asymptotic ratio (1000 terms)</a>

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

%F 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).

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

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

%Y Cf. A255322, A372240.

%Y Cf. A088021.

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Apr 23 2024