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

%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