cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A336991 Expansion of Product_{k>=1} (1 - x^k / (1 - k*x)).

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%I A336991 #14 Aug 10 2020 09:26:57
%S A336991 1,-1,-2,-3,-5,-10,-27,-91,-350,-1459,-6466,-30258,-149051,-771157,
%T A336991 -4181702,-23718221,-140437759,-866481074,-5561061327,-37066185842,
%U A336991 -256190732502,-1833581728979,-13571059095383,-103744579461855,-818183156375886,-6649600332967494,-55635988924348030
%N A336991 Expansion of Product_{k>=1} (1 - x^k / (1 - k*x)).
%F A336991 G.f.: exp( - Sum_{k>=1} x^k * Sum_{d|k} 1 / (d * (1 - k/d * x)^d)).
%t A336991 m = 26; CoefficientList[Series[Product[(1 - x^k/(1 - k*x)), {k, 1, m}], {x, 0, m}], x] (* _Amiram Eldar_, Aug 10 2020 *)
%o A336991 (PARI) N=40; x='x+O('x^N); Vec(prod(k=1, N, 1-x^k/(1-k*x)))
%o A336991 (PARI) N=40; x='x+O('x^N); Vec(exp(-sum(k=1, N, x^k*sumdiv(k, d, 1/(d*(1-k/d*x)^d)))))
%Y A336991 Convolution inverse of A336990.
%Y A336991 Cf. A307599, A336989.
%K A336991 sign
%O A336991 0,3
%A A336991 _Seiichi Manyama_, Aug 10 2020