A272238 - OEIS

%I #9 Apr 23 2016 07:36:54

%S 1,2,2073600,25177856146146034974720000000,

%T 14100949826093501607549529280892932893801777581548587107609477120000000000000000

%N a(n) = Product_{k=0..n} (n^2+k)!.

%C The next term has 173 digits.

%F a(n) = ((n^2+n)!)^(n+1) / A272237(n).

%F a(n) ~ exp(11/24 + n/6 - n^2 - n^3) * n^((1+n)*(1 + n + 2*n^2)) * (2*Pi)^((n+1)/2).

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

%t Table[BarnesG[n^2 + n + 2]/BarnesG[n^2 + 1], {n, 0, 6}]

%Y Cf. A135860, A272164, A272180, A272237, A272241.

%K nonn,easy

%O 0,2

%A _Vaclav Kotesovec_, Apr 23 2016