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A249386
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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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4
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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
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OFFSET
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0,1
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COMMENTS
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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]
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LINKS
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Steven Finch, Integer Partitions, September 22, 2004. [Cached copy, with permission of the author]
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FORMULA
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a = zeta(3)^(7/36)*exp(zeta'(-1))/(2^(11/36)*sqrt(3*Pi).
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EXAMPLE
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0.231516813448898370560356406406332110855129212593287926597944524...
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MATHEMATICA
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a = Zeta[3]^(7/36)*Exp[Zeta'[-1]]/(2^(11/36)*Sqrt[3*Pi]); RealDigits[a, 10, 104] // First
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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