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%I #8 Apr 02 2019 05:53:24
%S 1,1,2,3,6,8,15,20,34,48,76,103,165,222,335,461,683,919,1352,1813,
%T 2611,3519,4985,6651,9408,12501,17401,23165,32009,42312,58241,76748,
%U 104725,138017,187155,245521,332135,434536,584023,763799,1022507,1332549,1779534,2314437,3077540,3999825
%N Expansion of Product_{k>=1} 1/(1 - Sum_{j=1..k} x^(j*k)).
%H Vaclav Kotesovec, <a href="/A319758/b319758.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: Product_{k>=1} (1 - x^k)/(1 - 2*x^k + x^(k*(k+1))).
%F From _Vaclav Kotesovec_, Sep 27 2018: (Start)
%F a(n) ~ c * phi^(n/2), where
%F c = 188.4773924093125890061786423020365148584841831715... if n is even
%F c = 187.5693962190327254176348797865060646998844995050... if n is odd
%F phi = A001622 = (1+sqrt(5))/2 is the golden ratio. (End)
%p a:=series(mul(1/(1-add(x^(j*k),j=1..k)),k=1..100),x=0,46): seq(coeff(a,x,n),n=0..45); # _Paolo P. Lava_, Apr 02 2019
%t nmax = 45; CoefficientList[Series[Product[1/(1 - Sum[x^(j k), {j, 1, k}]), {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A052335, A115584.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Sep 27 2018