A368209 a(n) = Sum_{k=0..n} BarnesG(k)*BarnesG(n-k).

0, 0, 1, 2, 3, 6, 29, 604, 69724, 49836144, 250872492816, 10113420362487552, 3669877057922582621184, 13317216838086531218401935360, 531580547910000731718546175028428800, 254627927130379381409123944181515703549952000

Offset: 0

Author

Vaclav Kotesovec, Dec 17 2023

Keywords

• nonn

Links

• Eric Weisstein's World of Mathematics, Barnes G-Function.
• Wikipedia, Barnes G-function.

Crossrefs

Cf. A000178, A003149.

Programs

Mathematica

Table[Sum[BarnesG[k]*BarnesG[n-k], {k, 0, n}], {n, 0, 15}]

Formula

a(n) ~ 2^(n/2) * Pi^(n/2 - 1) * n^(n^2/2 - 2*n + 23/12) / (A * exp(3*n^2/4 - 2*n - 1/12)), where A = A074962 is the Glaisher-Kinkelin constant.