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A255439 Decimal expansion of a constant related to A255360. 4

%I #18 Nov 06 2016 01:40:01

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

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

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

%N Decimal expansion of a constant related to A255360.

%F Equals limit n->infinity (Product_{k=0..n} (k^5)!) / (n^(80/63 + 5*n/2 - 5*n^2/12 + 25*n^4/12 + 5*n^5/2 + (5*n^6)/6) * (2*Pi)^(n/2) / exp(5*n/2 + 35*n^2/144 + n^5/2 + 11*n^6/36)).

%F Equals 2^(5/4)*Pi^(5/4)*exp(137/3024 - 5*Zeta'(-5)) * Product_{n>=1} ((n^5)! / stirling(n^5)), where stirling(n^5) = sqrt(2*Pi) * n^(5*n^5 + 5/2) / exp(n^5) is the Stirling approximation of (n^5)! and Zeta'(-5) = A259070. - _Vaclav Kotesovec_, Apr 20 2016

%e 11.354954749729782312106630592450215781014...

%Y Cf. A255360, A255504, A255511, A255438.

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

%K nonn,cons

%O 2,3

%A _Vaclav Kotesovec_, Feb 24 2015

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Last modified March 28 14:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)