A296607 a(n) = BarnesG(2*n).

0, 1, 2, 288, 24883200, 5056584744960000, 6658606584104736522240000000, 127313963299399416749559771247411200000000000, 69113789582492712943486800506462734562847413501952000000000000000

Offset: 0

Author

Vaclav Kotesovec, Dec 16 2017

Keywords

• nonn

Links

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

Crossrefs

Cf. A000178, A098694, A296591, A296608, A306635.

Programs

Mathematica

Table[BarnesG[2*n], {n, 0, 10}]
Table[Glaisher^3 * E^(-1/4) * 2^(2*n^2 - 3*n + 11/12) * Pi^(1/2 - n) * BarnesG[n] * BarnesG[n + 1/2]^2 * BarnesG[n+1], {n, 0, 10}]

Formula

a(n) = A^3 * exp(-1/4) * 2^(2*n^2 - 3*n + 11/12) * Pi^(1/2 - n) * BarnesG(n) * BarnesG(n + 1/2)^2 * BarnesG(n+1), where A is the Glaisher-Kinkelin constant A074962.

a(n) ~ 2^(2*n^2 - n - 1/12) * exp(1/12 + 2*n - 3*n^2) * n^(2*n^2 - 2*n + 5/12) * Pi^(n - 1/2) / A, where A is the Glaisher-Kinkelin constant A074962.

a(n) = A000178(2*n-2), n>0. - R. J. Mathar, Jul 24 2025