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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)).
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%I #30 Jun 03 2017 15:33:36

%S 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,

%T 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,

%U 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

%N 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)).

%C 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]

%H G. C. Greubel, <a href="/A249386/b249386.txt">Table of n, a(n) for n = 0..5000</a>

%H Steven Finch, <a href="/A000219/a000219_1.pdf">Integer Partitions</a>, September 22, 2004. [Cached copy, with permission of the author]

%H L. Mutafchiev and E. Kamenov, <a href="http://arXiv.org/abs/math.CO/0601253">On The Asymptotic Formula for the Number of Plane Partitions...</a>, C. R. Acad. Bulgare Sci. 59(2006), No. 4, 361-366.

%F a = zeta(3)^(7/36)*exp(zeta'(-1))/(2^(11/36)*sqrt(3*Pi).

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

%e 0.231516813448898370560356406406332110855129212593287926597944524...

%t a = Zeta[3]^(7/36)*Exp[Zeta'[-1]]/(2^(11/36)*Sqrt[3*Pi]); RealDigits[a, 10, 104] // First

%Y Cf. A000219, A020805, A084448, A239049.

%K nonn,cons,easy

%O 0,1

%A _Jean-François Alcover_, Oct 27 2014