A399340 - OEIS

A399340

a(n) = Product_{j=0..n-1} binomial(n + j, n).

1, 1, 3, 40, 2625, 889056, 1597337280, 15499944345600, 822671773729430625, 241085200067671960000000, 392931723549413089537198230528, 3582424004893029152699939723044454400, 183567545325759226366323287047570517936640000, 53072894914980586427544217999469521617892147200000000

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

Table of n, a(n) for n=0..13.

FORMULA

a(n) * n!^n = a(n) * A036740(n) = A107254(n).

For n > 0, a(n) = BarnesG(2*n) * Gamma(2*n) / (BarnesG(n)^2 * Gamma(n)^(n+2) * n^n). - Vaclav Kotesovec, Sep 03 2026

MAPLE

a := n -> mul(binomial(n + j, n), j = 0..n-1): seq(a(n), n = 0..13);

MATHEMATICA

Join[{1}, Table[BarnesG[2*n] * Gamma[2*n] / (BarnesG[n]^2 * Gamma[n]^(n+2) * n^n), {n, 1, 13}]] (* Vaclav Kotesovec, Sep 03 2026 *)