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%I #23 May 10 2018 09:38:29
%S 1,1,0,2,0,1,3,1,1,2,6,1,4,2,5,10,5,4,9,7,8,21,9,13,13,19,13,27,32,23,
%T 29,33,27,45,37,45,79,49,57,68,82,67,101,83,109,155,124,113,174,148,
%U 171,196,215,198,262,310,269,330,314,342,414,430,393,536,493
%N Expansion of Product_{k>=1} (1 + x^k - x^(2*k)).
%H Vaclav Kotesovec, <a href="/A263401/b263401.txt">Table of n, a(n) for n = 0..5000</a>
%F a(n) ~ sqrt(log(phi)) * phi^sqrt(8*n) / (2^(3/4)*sqrt(Pi)*n^(3/4)), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - _Vaclav Kotesovec_, Jan 03 2016
%t nmax = 80; CoefficientList[Series[Product[1+x^k-x^(2*k), {k, 1, nmax}], {x, 0, nmax}], x]
%t nmax = 100; p = ConstantArray[0, nmax + 1]; p[[1]] = 1; p[[2]] = 1; p[[3]] = -1; Do[Do[p[[j+1]] = p[[j+1]] + p[[j - k + 1]] - If[j < 2*k, 0, p[[j - 2*k + 1]]], {j, nmax, k, -1}];, {k, 2, nmax}]; p (* _Vaclav Kotesovec_, May 10 2018 *)
%Y Cf. A000726, A002390, A055922, A100847, A109389, A162891, A266686.
%K nonn
%O 0,4
%A _Vaclav Kotesovec_, Jan 03 2016
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