editing

approved

a(n) = 4*n*Gamma(2*n)^2 * A368685(n) / (4*n*Gamma(2*n)^2).

allocated for Vaclav Kotesovec

a(n) = Product_{j=0..n, k=0..n} (j + k + n).

0, 12, 172800, 1536288768000, 16189465114548633600000, 322110526445545505917029580800000000, 17555281051920416386104936570114748195012608000000000, 3580285185706909590176164870311607533516764550107699116769280000000000000

0,2

For n>0, a(n) = 3*n*BarnesG(n) * BarnesG(3*n) * Gamma(3*n)^2 / BarnesG(2*n+1)^2.

a(n) ~ 3^(9*n^2/2 + 3*n + 5/12) * n^((n+1)^2) / (2^(4*n^2 - 1/6) * exp(3*n^2/2 + 2*n)).

a(n) = Gamma(n)^2 * A368685(n) / (4*n*Gamma(2*n)^2).

Table[Product[i+j+n, {i, 0, n}, {j, 0, n}], {n, 0, 8}]

Join[{0}, Table[3*n*BarnesG[n] * BarnesG[3*n] * Gamma[3*n]^2 / BarnesG[2*n+1]^2, {n, 1, 8}]]

Cf. A079478, A306594, A324444, A368622, A368685.

allocated

nonn

Vaclav Kotesovec, Jan 03 2024

approved

editing

allocated for Vaclav Kotesovec

allocated

approved