%I #13 Nov 16 2016 03:03:39

%S 1,0,1,1,2,2,5,4,9,10,17,19,34,37,61,75,112,138,209,256,376,478,675,

%T 866,1222,1566,2175,2830,3873,5055,6900,9011,12213,16045,21599,28429,

%U 38191,50290,67341,88884,118669,156751,209018,276200,367734,486376,646688

%N Expansion of Product_{k>=1} 1/(1 - x^(2*k) - x^(3*k)).

%H Vaclav Kotesovec, <a href="/A276519/b276519.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) ~ c * p / r^n, where r = A075778 = 1/A060006 = 0.7548776662466927600495... is the real root of the equation r^3 + r^2 - 1 = 0, p = Product_{n>1} 1/(1 - r^(2*n) - r^(3*n)) = 3.820450591662541853... and c = 0.41149558866264576338190038... is the real root of the equation -1 + 8*c - 23*c^2 + 23*c^3 = 0.

%t nmax=50; CoefficientList[Series[1/Product[1-x^(2*k)-x^(3*k), {k, 1, nmax}], {x, 0, nmax}], x]

%Y Cf. A264905, A266686, A275820, A275821, A276526.

%K nonn

%O 0,5

%A _Vaclav Kotesovec_, Nov 15 2016