A249389 Decimal expansion of the constant 'B' appearing in the asymptotic expression of the number of partitions of n as (B/(2*Pi*n))*exp(2*B*sqrt(n)), in case of partitions into integers, each of which occurring only an odd number of times.
1, 1, 3, 3, 8, 4, 1, 5, 5, 6, 2, 0, 5, 4, 9, 6, 4, 6, 6, 7, 3, 3, 7, 6, 8, 6, 3, 2, 4, 6, 0, 5, 0, 1, 9, 3, 1, 2, 0, 6, 0, 2, 9, 6, 2, 8, 8, 0, 8, 6, 5, 4, 0, 1, 0, 4, 1, 7, 3, 8, 0, 6, 7, 2, 7, 8, 0, 8, 4, 7, 5, 5, 1, 2, 5, 9, 1, 7, 9, 4, 5, 8, 5, 8, 3, 6, 2, 1, 1, 9, 0, 6, 3, 3, 9, 5, 9, 6, 2
Offset: 1
Examples
1.133841556205496466733768632460501931206029628808654...
Links
- G. C. Greubel, Table of n, a(n) for n = 1..10000
- F. C. Auluck, K. S. Singwi and B. K. Agarwala, On a new type of partition, Proc. Nat. Inst. Sci. India 16 (1950) 147-156.
- Steven Finch, Integer Partitions, September 22, 2004. [Cached copy, with permission of the author]
Programs
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Mathematica
B = Sqrt[Pi^2/12 + 2*Log[GoldenRatio]^2]; RealDigits[B, 10, 99] // First
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PARI
sqrt(Pi^2/12 + 2*(log((1+sqrt(5))/2))^2) \\ G. C. Greubel, Apr 06 2017
Formula
B = sqrt(Pi^2/12 + 2*log(phi)^2), where phi is the golden ratio.