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A255504
Decimal expansion of a constant related to A255322.
8
3, 0, 4, 8, 3, 3, 0, 3, 0, 6, 5, 2, 2, 3, 4, 8, 5, 6, 6, 9, 1, 1, 9, 2, 0, 4, 1, 7, 3, 3, 7, 6, 1, 3, 0, 1, 5, 8, 8, 5, 3, 1, 3, 4, 7, 5, 6, 8, 9, 0, 4, 9, 1, 8, 4, 5, 2, 5, 4, 8, 3, 6, 9, 7, 6, 8, 4, 8, 3, 4, 1, 6, 5, 3, 3, 9, 0, 8, 8, 1, 4, 5, 1, 4, 6, 6, 7, 7, 6, 7, 0, 2, 2, 1, 6, 0, 5, 1, 6, 7, 7, 1, 9, 1, 8
OFFSET
1,1
FORMULA
Equals limit n->infinity (Product_{k=0..n} (k^2)!) / (n^((2*n + 1)*(2*n^2 + 2*n + 3)/6) * (2*Pi)^(n/2) / exp(5*n^3/9 + n^2/2 + n)).
Equals sqrt(2*Pi) * exp(Zeta(3)/(2*Pi^2)) * Product_{n>=1} ((n^2)!/stirling(n^2)), where stirling(n^2) = sqrt(2*Pi) * n^(2*n^2+1) / exp(n^2) is the Stirling approximation of (n^2)!. - Vaclav Kotesovec, Apr 20 2016
EXAMPLE
3.048330306522348566911920417337613015885313475689049184525483697684834...
KEYWORD
nonn,cons
AUTHOR
Vaclav Kotesovec, Feb 24 2015
STATUS
approved