A249386 Decimal expansion of the constant 'a' appearing in the asymptotic expression of the number of plane partitions of n as a*n^(-25/36)*exp(b*n^(2/3)).

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

Offset: 0

Author

Jean-François Alcover, Oct 27 2014

Keywords

• nonn
• cons
• easy

Comments

The paper by Finch contains an error: the denominator should be sqrt(3*Pi), not sqrt(Pi). The constant 0.4009988836 is wrong. The formula in A000219 and the article by L. Mutafchiev and E. Kamenov (page 6) is correct. - Vaclav Kotesovec, Oct 27 2014. [In new version of prt.pdf is already corrected. - Vaclav Kotesovec, May 11 2015]

Examples

			0.231516813448898370560356406406332110855129212593287926597944524...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..5000
• Steven Finch, Integer Partitions, September 22, 2004. [Cached copy, with permission of the author]
• L. Mutafchiev and E. Kamenov, On The Asymptotic Formula for the Number of Plane Partitions of Positive Integers, arXiv:math/0601253 [math.CO], 2006; C. R. Acad. Bulgare Sci. 59(2006), No. 4, 361-366.

Crossrefs

Cf. A000219, A020805, A084448, A239049.

Programs

Mathematica

a = Zeta[3]^(7/36)*Exp[Zeta'[-1]]/(2^(11/36)*Sqrt[3*Pi]); RealDigits[a, 10, 104] // First

Formula

Equals zeta(3)^(7/36)*exp(zeta'(-1))/(2^(11/36)*sqrt(3*Pi)).

Equals exp(1/12) * A002117^(7/36) / (A074962 * 2^(11/36) * sqrt(3*Pi)). - Vaclav Kotesovec, Mar 02 2015