%I #16 Aug 10 2020 09:26:21
%S 1,1,2,5,13,36,107,343,1184,4391,17448,74082,335131,1610301,8191728,
%T 43973853,248305235,1470474074,9107950029,58856529464,395914407606,
%U 2766669954699,20047716439541,150384068021507,1166037568730402,9332538119883810,77004693701288392,654279226353488820
%N Expansion of Product_{k>=1} (1 + x^k / (1 - k*x)).
%F G.f.: exp(Sum_{k>=1} x^k * Sum_{d|k} (-1)^(d+1) / (d * (1 - k/d * x)^d)).
%t m = 27; CoefficientList[Series[Product[1 + x^k/(1 - k*x), {k, 1, m}], {x, 0, m}], x] (* _Amiram Eldar_, Aug 10 2020 *)
%o (PARI) N=40; x='x+O('x^N); Vec(prod(k=1, N, 1+x^k/(1-k*x)))
%o (PARI) N=40; x='x+O('x^N); Vec(exp(sum(k=1, N, x^k*sumdiv(k, d, (-1)^(d+1)/(d*(1-k/d*x)^d)))))
%Y Cf. A126348, A336980, A336990, A336991.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Aug 10 2020