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

%I

%S 1,0,3,4,11,18,42,70,144,248,466,802,1442,2444,4247,7116,12030,19878,

%T 32938,53670,87429,140680,225815,359100,569157,895224,1402941,2184662,

%U 3388915,5228458,8035921,12291710,18732318,28425342,42981877,64740330

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

%H 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 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%F Euler transform of sequence [0, 3, 4, 5, 6, ...].

%F G.f.: Product_{k=2..infinity} 1/(1-x^k)^(k+1).

%F From _Vaclav Kotesovec_, Mar 09 2015: (Start)

%F For n>=2, a(n) = A005380(n-2) - 2*A005380(n-1) + A005380(n).

%F 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 a(n) ~ (2*Zeta(3))^(2/3) * A005380(n) / n^(2/3).

%F (End)

%t nmax=50; CoefficientList[Series[Product[1/(1-x^k)^(k+1),{k,2,nmax}],{x,0,nmax}],x] (* _Vaclav Kotesovec_, Mar 04 2015 *)

%Y Cf. (row sums of) A060244, A054225, A005380.

%K easy,nonn

%O 0,3

%A _Vladeta Jovovic_, Mar 23 2001

%E Edited by _Christian G. Bower_, Jan 08 2004

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Last modified June 20 00:47 EDT 2019. Contains 324223 sequences. (Running on oeis4.)