A368685 a(n) = Product_{j=1..n, k=1..n} (j + k + n).

1, 3, 600, 35562240, 1434015830016000, 70448433354492434841600000, 6610702315560389323908439364075520000000, 1709479709147705756603303596364188306401499545600000000000, 1660017838341811463102474357555838707949172571314554168163386261504000000000000

Offset

0,2

Links

Table of n, a(n) for n=0..8.

Formula

For n>0, a(n) = 3*BarnesG(n) * BarnesG(3*n) * Gamma(n)^2 * Gamma(3*n)^2 / (4*BarnesG(2*n)^2 * Gamma(2*n)^4).

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

Mathematica

Table[Product[i+j+n, {i, 1, n}, {j, 1, n}], {n, 0, 8}]
Join[{1}, Table[3*BarnesG[n] * BarnesG[3*n] * Gamma[n]^2 * Gamma[3*n]^2 / (4*BarnesG[2*n]^2 * Gamma[2*n]^4), {n, 1, 8}]]

Crossrefs

Cf. A079478, A306594, A324444, A368622, A368686.

Sequence in context: A203748 A329706 A229748 * A225761 A140029 A161964

Adjacent sequences: A368682 A368683 A368684 * A368686 A368687 A368688

Keyword

nonn

Author

Vaclav Kotesovec, Jan 03 2024

Status

approved