A255439 Decimal expansion of a constant related to A255360.

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

Offset: 2

Author

Vaclav Kotesovec, Feb 24 2015

Keywords

• nonn
• cons

Examples

			11.354954749729782312106630592450215781014...
		

Crossrefs

Cf. A255360, A255504, A255511, A255438.

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

Formula

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)).

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