|
%I #6 Mar 27 2019 07:39:38
%S 2,256,19131876000000,
%T 20879156515576282948808247752954619590255260568062500000000
%N a(n) = Product_{i=0..n, j=0..n, k=0..n} (i!*j!*k! + 1).
%C Next term is too long to be included.
%F 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...
%t Table[Product[i!*j!*k! + 1, {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 5}]
%t 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}]
%Y Cf. A306907, A325049.
%K nonn
%O 0,1
%A _Vaclav Kotesovec_, Mar 26 2019
|
