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

1,1

Links

Table of n, a(n) for n=1..105.

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

Example

4.113740552015338123052453340090368136395763815194771589658140463089224...

Crossrefs

Cf. A255358, A255504, A255438, A255439.

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

Sequence in context: A174834 A100642 A320438 * A014518 A316584 A362856

Adjacent sequences: A255508 A255509 A255510 * A255512 A255513 A255514

Keyword

nonn,cons

Author

Vaclav Kotesovec, Feb 24 2015

Status

approved