A371468 -id:A371468 - cp's OEIS frontend

A371643 a(n) = Product_{k=0..n} (n^2 + k^2)!.

1, 2, 116121600, 52498561358549216844165257625600000000

Offset: 0

Vaclav Kotesovec, Mar 31 2024

nonn

The next term has 107 digits.

Table[Product[(n^2+k^2)!, {k, 0, n}], {n, 0, 5}]

a(n) ~ 2^(4*n^3/3 + n^2 + 7*n/6 + 3/4) * exp(-26*n^3/9 + Pi*n^3/3 - 3*n^2/2 + Pi*n/4 - n) * Pi^((n+1)/2) * n^(8*n^3/3 + 3*n^2 + 4*n/3 + 1).

A371646 a(n) = Product_{k=0..n} binomial(n^3, k^3).

Original entry on oeis.org

1, 1, 8, 59942025, 239830737497318918172122578944, 788243862228623056807478850630904903414781894638966172447366478063616699218750

Offset: 0

Vaclav Kotesovec, Mar 31 2024

nonn

Cf. A001142, A371603.

Cf. A007685, A255358, A371468.

Table[Product[Binomial[n^3, k^3], {k, 0, n}], {n, 0, 6}]

a(n) ~ c * exp((9/4 - sqrt(3)*Pi/8)*n^4 + (3*zeta(3)/(4*Pi^2) - Pi/(4*sqrt(3)) + 3)*n) / ((2*Pi)^(n/2) * A^(3*n^2) * 3^(9*n^4/8 - n^2/4 + 3*n/4) * n^(n^2/4 + 3*n/2 - 8/15)), where c = 0.498332919... and A is the Glaisher-Kinkelin constant A074962.

cp's OEIS Frontend

A371643 a(n) = Product_{k=0..n} (n^2 + k^2)!.

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

Formula