%I #11 Nov 07 2019 04:08:44
%S 1,1,4,10,29,72,200,510,1364,3546,9348,24400,64090,167562,439200,
%T 1149360,3010349,7879832,20633304,54014950,141422328,370239300,
%U 969323000,2537696160,6643839400,17393731933,45537549048,119218684970,312119004990,817137724392,2139295489200,5600747143950
%N Expansion of Product_{k>=1} 1 / (1 - Sum_{j>=1} j * x^(k*j)).
%C Euler transform of A032198.
%F G.f.: Product_{k>=1} 1 / (1 - x^k / (1 - x^k)^2).
%F G.f.: exp(Sum_{k>=1} ( Sum_{d|k} 1 / (d * (1 - x^(k/d))^(2*d)) ) * x^k).
%F G.f.: Product_{k>=1} 1 / (1 - x^k)^A032198(k).
%F G.f.: A(x) = Product_{k>=1} B(x^k), where B(x) = g.f. of A088305.
%F a(n) ~ phi^(2*n-1), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - _Vaclav Kotesovec_, Nov 07 2019
%t nmax = 31; CoefficientList[Series[Product[1/(1 - Sum[j x^(k j), {j, 1, nmax}]), {k, 1, nmax}], {x, 0, nmax}], x]
%t nmax = 31; CoefficientList[Series[Product[1/(1 - x^k/(1 - x^k)^2), {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A006951, A032198, A088305, A162891, A258210, A329157, A329163.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Nov 06 2019