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Expansion of Product_{k>=1} 1/(1 - k*(x^(2*k-1))).
2

%I #6 Dec 21 2015 16:20:05

%S 1,1,1,3,3,6,10,14,20,33,50,68,106,147,214,325,445,624,916,1259,1780,

%T 2553,3477,4821,6794,9340,12777,17808,24266,32998,45764,61770,83593,

%U 114594,154039,208617,283232,379040,509270,687448,919709,1228319,1650595,2195745

%N Expansion of Product_{k>=1} 1/(1 - k*(x^(2*k-1))).

%H Vaclav Kotesovec, <a href="/A266137/b266137.txt">Table of n, a(n) for n = 0..9850</a>

%F a(n) ~ c * 2^(n/3), where

%F c = 2684.3207660224428945778151546260301591494083790... if mod(n,3) = 0

%F c = 2683.9203893332021512699407898064547843826991184... if mod(n,3) = 1

%F c = 2683.7635451650373491773203224442103370428384569... if mod(n,3) = 2.

%t nmax=60; CoefficientList[Series[Product[1/(1-k*(x^(2*k-1))), {k, 1, nmax}], {x, 0, nmax}], x]

%Y Cf. A000009, A006906, A077335, A265951, A266138.

%K nonn

%O 0,4

%A _Vaclav Kotesovec_, Dec 21 2015