A255511 Decimal expansion of a constant related to A255358.

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, 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, 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

Offset: 1

Author

Vaclav Kotesovec, Feb 24 2015

Keywords

• nonn
• cons

Examples

			4.113740552015338123052453340090368136395763815194771589658140463089224...
		

Crossrefs

Cf. A255358, A255504, A255438, A255439.

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

Formula

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)).

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