A272167 - OEIS

%I #13 Apr 21 2024 07:21:10

%S 1,4,864,17915904,57330892800000,41794220851200000000000,

%T 9635211808655307020697600000000000,

%U 931891782579353562478377930946353561600000000000,48457159197906991133853954271145046614004301737177907200000000000

%N a(n) = Product_{k=2..n} (k^2-k)^k.

%F a(n) ~ A^2 * sqrt(2*Pi) * n^(n^2 + n - 1/3) / exp(n*(n+2)/2), where A = A074962 is the Glaisher-Kinkelin constant.

%F a(n) = n^n * Gamma(n)^(2*n-1) / BarnesG(n)^2. - _Vaclav Kotesovec_, Apr 21 2024

%t Table[Product[(k^2-k)^k, {k, 2, n}], {n, 1, 10}]

%t Table[n^n * Gamma[n]^(2*n-1) / BarnesG[n]^2, {n,1,10}] (* _Vaclav Kotesovec_, Apr 21 2024 *)

%o (PARI) a(n) = prod(k=2, n, (k^2-k)^k); \\ _Michel Marcus_, Nov 18 2021

%Y Cf. A002109, A272168.

%K nonn,easy

%O 1,2

%A _Vaclav Kotesovec_, Apr 21 2016

%E Definition corrected by _Georg Fischer_, Nov 18 2021