A272237 a(n) = Product_{k=0..n} (n^2+k)^k.

2, 180, 2090880, 6044699520000, 7151106328088486400000, 5159620144413185246982598164480000, 3167269298042065159436486399933762922086400000000, 2200712918907364598767850489247066133407004510957047455416320000000

Offset: 1

Author

Vaclav Kotesovec, Apr 23 2016

Keywords

• nonn
• easy

Crossrefs

Cf. A272163, A272180, A272238.

Programs

Mathematica

Table[Product[(n^2+k)^k, {k, 0, n}], {n, 1, 10}]
Table[((n^2+n)!)^(n+1) * BarnesG[n^2 + 1] / BarnesG[n^2 + n + 2], {n, 1, 10}]

Formula

a(n) = ((n^2+n)!)^(n+1) / A272238(n).

a(n) ~ exp(n/3 + 3/8) * n^(n*(n+1)).