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.

A306327 Expansion of Product_{k>=1} 1/(1 - mu(k)*x^k), where mu() is the Möbius function (A008683).

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%I A306327 #6 Feb 08 2019 05:19:09
%S A306327 1,1,0,-1,0,0,1,0,0,-1,2,0,1,-2,2,0,4,-4,1,-4,6,-2,8,-8,6,-7,13,-10,
%T A306327 13,-16,17,-17,22,-25,29,-26,40,-37,40,-50,58,-56,69,-75,82,-90,108,
%U A306327 -110,128,-133,158,-168,185,-207,229,-238,281,-298,328,-357,405,-417,477,-518,564,-608
%N A306327 Expansion of Product_{k>=1} 1/(1 - mu(k)*x^k), where mu() is the Möbius function (A008683).
%H A306327 Vaclav Kotesovec, <a href="/A306327/b306327.txt">Table of n, a(n) for n = 0..10000</a>
%F A306327 G.f.: exp(Sum_{k>=1} Sum_{j>=1} mu(j)^k*x^(j*k)/k).
%t A306327 nmax = 65; CoefficientList[Series[Product[1/(1 - MoebiusMu[k] x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%t A306327 nmax = 65; CoefficientList[Series[Exp[Sum[Sum[MoebiusMu[j]^k x^(j k)/k, {j, 1, nmax}], {k, 1, nmax}]], {x, 0, nmax}], x]
%t A306327 a[n_] := a[n] = If[n == 0, 1, Sum[Sum[d MoebiusMu[d]^(k/d), {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 65}]
%Y A306327 Cf. A008683, A073576, A117209.
%K A306327 sign
%O A306327 0,11
%A A306327 _Ilya Gutkovskiy_, Feb 07 2019