A249389 - OEIS

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.

%I #18 Jul 22 2020 11:42:35

%S 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,

%T 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,

%U 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

%N 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.

%H G. C. Greubel, <a href="/A249389/b249389.txt">Table of n, a(n) for n = 1..10000</a>

%H F. C. Auluck, K. S. Singwi and B. K. Agarwala, <a href="http://www.dli.gov.in/data_copy/upload/INSA/INSA_2/20005a88_147.pdf">On a new type of partition</a>, Proc. Nat. Inst. Sci. India 16 (1950) 147-156.

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

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

%e 1.133841556205496466733768632460501931206029628808654...

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

%o (PARI) sqrt(Pi^2/12 + 2*(log((1+sqrt(5))/2))^2) \\ _G. C. Greubel_, Apr 06 2017

%Y Cf. A000041, A002390, A055922.

%K nonn,cons,easy

%O 1,3

%A _Jean-François Alcover_, Oct 27 2014