A255939 Decimal expansion of a constant related to A000294.

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

Offset

0,1

Comments

The unknown constant C from articles by Finch (p.2), resp. c3(m) by Mustonen and Rajesh (p.2).

Links

Table of n, a(n) for n=0..105.

Steven Finch, Integer Partitions, September 22, 2004, page 2. [Cached copy, with permission of the author].

Ville Mustonen and R. Rajesh, Numerical Estimation of the Asymptotic Behaviour of Solid Partitions of an Integer, J. Phys. A 36 (2003), no. 24, 6651-6659.

Formula

Equals Pi^(1/24) * exp(1/24 - Zeta(3) / (8*Pi^2) + 75*Zeta(3)^3 / (2*Pi^8)) / (A^(1/2) * 2^(157/96) * 15^(13/96)), where A = A074962 is the Glaisher-Kinkelin constant and Zeta(3) = A002117.

Example

0.213595160470700180128341262729125127820323477061218341828788505264420561...

Mathematica

RealDigits[Pi^(1/24) * E^(1/24 - Zeta[3]/(8*Pi^2) + 75*Zeta[3]^3/(2*Pi^8)) / (Glaisher^(1/2)*2^(157/96)*15^(13/96)), 10, 120][[1]]

Crossrefs

Cf. A000294, A002117, A074962.

Sequence in context: A263047 A021828 A094341 * A333177 A169912 A316994

Adjacent sequences: A255936 A255937 A255938 * A255940 A255941 A255942

Keyword

nonn,cons

Author

Vaclav Kotesovec, Mar 11 2015

Status

approved