%I #4 Oct 05 2017 11:33:56

%S 1,1,2,1,1,3,3,5,6,4,6,8,11,13,13,18,19,23,29,32,35,40,48,51,65,78,86,

%T 96,102,121,142,162,179,199,220,251,289,323,359,395,450,499,562,631,

%U 695,762,840,952,1055,1167,1292,1413,1557,1733,1903,2112,2323,2534

%N Expansion of Product_{k>=1} (1 + x^(2*k-1) + 2*x^(4*k-2)).

%H Vaclav Kotesovec, <a href="/A293304/b293304.txt">Table of n, a(n) for n = 0..2000</a>

%F a(n) ~ c^(1/4) * exp(sqrt(2*c*n)) / (2^(5/4) * sqrt(Pi) * n^(3/4)), where c = -polylog(2, -1/2 + I*sqrt(7)/2) - polylog(2, -1/2 - I*sqrt(7)/2) = 1.323865936864425754643630663383779192757247984691212163137...

%t nmax = 100; CoefficientList[Series[Product[(1 + x^(2*k-1) + 2*x^(4*k-2)), {k, 1, nmax}], {x, 0, nmax}], x]

%Y Cf. A293072.

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Oct 05 2017