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

1,3

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]

Formula

B = sqrt(Pi^2/12 + 2*log(phi)^2), where phi is the golden ratio.

Example

1.133841556205496466733768632460501931206029628808654...

Mathematica

B = Sqrt[Pi^2/12 + 2*Log[GoldenRatio]^2]; RealDigits[B, 10, 99] // First

Prog

(PARI) sqrt(Pi^2/12 + 2*(log((1+sqrt(5))/2))^2) \\ G. C. Greubel, Apr 06 2017

Crossrefs

Cf. A000041, A002390, A055922.

Sequence in context: A143615 A199337 A279789 * A016606 A341616 A069462

Adjacent sequences: A249386 A249387 A249388 * A249390 A249391 A249392

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Oct 27 2014

Status

approved