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Decimal expansion of a constant related to A255359.
4

%I #15 Apr 20 2016 07:22:19

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

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

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

%N Decimal expansion of a constant related to A255359.

%F Equals limit n->infinity (Product_{k=0..n} (k^4)!) / (n^(1 + 28*n/15 + 4*n^3/3 + 2*n^4 + 4*n^5/5) * (2*Pi)^(n/2) / exp(19*n/9 + n^4/2 + 9*n^5/25)).

%F Equals 2*Pi*exp(-3*Zeta(5)/Pi^4) * Product_{n>=1} ((n^4)!/stirling(n^4)), where stirling(n^4) = sqrt(2*Pi) * n^(4*n^4 + 2) / exp(n^4) is the Stirling approximation of (n^4)! and Zeta(5) = A013663. - _Vaclav Kotesovec_, Apr 20 2016

%e 6.644987918706354049483118316737842660075362652005201561326290428710371...

%Y Cf. A255359, A255504, A255511, A255439.

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

%K nonn,cons

%O 1,1

%A _Vaclav Kotesovec_, Feb 24 2015