OFFSET
0,1
COMMENTS
Next term is too long to be included.
FORMULA
a(n) ~ c * (2*Pi)^(3*n^3/2 + 9*n^2/2 + 9*n/2 + 3/2) * n^((n+1)^2*(6*n^2 + 12*n + 5)/4) / (A^(3*(n+1)^2) * exp(9*n^4/4 + 15*n^3/2 + 8*n^2 + 9*n/4 - 59/80)), where A is the Glaisher-Kinkelin constant A074962 and c = Product_{i>=0, j>=0, k>=0} (1 + 1/(i!*j!*k!)) = 10013049.64089403856780758322163675337812476527762657951330...
MATHEMATICA
Table[Product[i!*j!*k! + 1, {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 5}]
Table[BarnesG[n+2]^(3*(n+1)^2) * Product[1 + 1/(i!*j!*k!), {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 5}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Mar 26 2019
STATUS
approved