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%I #8 Nov 16 2016 03:03:30
%S 1,0,1,-1,2,-2,3,-4,7,-8,11,-15,22,-27,37,-51,70,-90,121,-162,220,
%T -288,381,-512,688,-902,1197,-1598,2127,-2809,3722,-4949,6581,-8699,
%U 11519,-15301,20305,-26862,35581,-47208,62591,-82859,109756,-145506,192856,-255388
%N Expansion of Product_{k>=1} 1/(1 - x^(2*k) + x^(3*k)).
%H Vaclav Kotesovec, <a href="/A276526/b276526.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) ~ c * p / r^n, where r = -A075778 = -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)) = 1.9844809074648434... 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, A276519.
%K sign
%O 0,5
%A _Vaclav Kotesovec_, Nov 16 2016