A272096 a(n) = Product_{k=0..n} (k*n)!.

1, 1, 48, 1567641600, 9698137182219213471744000000, 21488900044302744250061179567064173417691432878080000000000000000

Offset

0,3

Comments

The next term has 126 digits.

Links

Table of n, a(n) for n=0..5.

Formula

a(n) ~ A^n * n^(1/4 + 13*n/12 + n^2 + n^3) * (2*Pi)^(1/4 + n/2) / exp(n*(2 + 2*n + 3*n^2)/4), where A = A074962 is the Glaisher-Kinkelin constant.

Mathematica

Table[Product[(k*n)!, {k, 0, n}], {n, 0, 6}]

Crossrefs

Cf. A000178, A098694, A268504, A268505, A268506, A271946.

Cf. A255322, A272093.

Sequence in context: A165047 A291865 A292517 * A115480 A214953 A005071

Adjacent sequences: A272093 A272094 A272095 * A272097 A272098 A272099

Keyword

nonn,easy

Author

Vaclav Kotesovec, Apr 20 2016

Status

approved