OFFSET
0,3
FORMULA
a(n) ~ c1/c2 * A * exp(-1/12 + n/2 + n^2/4) * n^(1/12 + n^2/2) / (2*Pi)^(n/2), where c1 = Product_{k>=1} (k^2)!/stirling(k^2) = 1.14426047263759216966268786..., c2 = Product_{k>=2} (k*(k-1))!/stirling(k*(k-1)) = 1.086533635964823338078329..., stirling(n) = sqrt(2*Pi*n) * n^n / exp(n) is the Stirling approximation of n!, and A = A074962 is the Glaisher-Kinkelin constant.
MATHEMATICA
Table[Product[Binomial[k^2, k], {k, 0, n}], {n, 0, 10}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vaclav Kotesovec, Apr 20 2016
STATUS
approved