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Decimal expansion of a constant related to A255358.
4

%I #9 Apr 20 2016 06:41:48

%S 4,1,1,3,7,4,0,5,5,2,0,1,5,3,3,8,1,2,3,0,5,2,4,5,3,3,4,0,0,9,0,3,6,8,

%T 1,3,6,3,9,5,7,6,3,8,1,5,1,9,4,7,7,1,5,8,9,6,5,8,1,4,0,4,6,3,0,8,9,2,

%U 2,4,5,4,0,6,0,1,1,4,8,1,3,0,0,8,7,7,9,8,9,6,1,4,7,9,4,3,0,0,4,4,8,2,9,6,8

%N Decimal expansion of a constant related to A255358.

%F Equals limit n->infinity (Product_{k=0..n} (k^3)!) / (n^(29/40 + 3*n/2 + 3*n^2/4 + 3*n^3/2 + 3*n^4/4) * (2*Pi)^(n/2) / exp(n*(n+2)*(12 - 6*n + 7*n^2)/16)).

%F Equals (2*Pi)^(3/4) * exp(-11/240 - 3*Zeta'(-3)) * Product_{n>=1} ((n^3)!/stirling(n^3)), where stirling(n^3) = sqrt(2*Pi) * n^(3*n^3 + 3/2) / exp(n^3) is the Stirling approximation of (n^3)! and Zeta'(-3) = A259068. - _Vaclav Kotesovec_, Apr 20 2016

%e 4.113740552015338123052453340090368136395763815194771589658140463089224...

%Y Cf. A255358, A255504, A255438, A255439.

%Y Cf. A074962, A243262, A243263, A243264, A243265.

%K nonn,cons

%O 1,1

%A _Vaclav Kotesovec_, Feb 24 2015