cp's OEIS Frontend

A060285 Number of partitions of n objects of 2 colors with parts size >1.

%I A060285 #28 Jan 29 2019 15:09:47
%S A060285 1,0,3,4,11,18,42,70,144,248,466,802,1442,2444,4247,7116,12030,19878,
%T A060285 32938,53670,87429,140680,225815,359100,569157,895224,1402941,2184662,
%U A060285 3388915,5228458,8035921,12291710,18732318,28425342,42981877,64740330
%N A060285 Number of partitions of n objects of 2 colors with parts size >1.
%H A060285 Alois P. Heinz, <a href="/A060285/b060285.txt">Table of n, a(n) for n = 0..10000</a> (first 1001 terms from Vaclav Kotesovec)
%H A060285 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F A060285 Euler transform of sequence [0, 3, 4, 5, 6, ...].
%F A060285 G.f.: Product_{k=2..infinity} 1/(1-x^k)^(k+1).
%F A060285 From _Vaclav Kotesovec_, Mar 09 2015: (Start)
%F A060285 For n>=2, a(n) = A005380(n-2) - 2*A005380(n-1) + A005380(n).
%F A060285 a(n) ~ 2^(1/36) * Zeta(3)^(37/36) * exp(1/12 - Pi^4/(432*Zeta(3)) + Pi^2 * n^(1/3) / (3*2^(4/3)*Zeta(3)^(1/3)) + 3*Zeta(3)^(1/3) * n^(2/3) / 2^(2/3)) / (A * 3^(1/2) * Pi * n^(55/36)), where A = A074962 = 1.2824271291... is the Glaisher-Kinkelin constant and Zeta(3) = A002117 = 1.202056903... .
%F A060285 a(n) ~ (2*Zeta(3))^(2/3) * A005380(n) / n^(2/3).
%F A060285 (End)
%t A060285 nmax=50; CoefficientList[Series[Product[1/(1-x^k)^(k+1),{k,2,nmax}],{x,0,nmax}],x] (* _Vaclav Kotesovec_, Mar 04 2015 *)
%Y A060285 Cf. (row sums of) A060244, A054225, A005380.
%K A060285 easy,nonn
%O A060285 0,3
%A A060285 _Vladeta Jovovic_, Mar 23 2001
%E A060285 Edited by _Christian G. Bower_, Jan 08 2004