cp's OEIS Frontend

A320783 Inverse Euler transform of (-1)^(n - 1).

%I A320783 #4 Oct 22 2018 22:55:03
%S A320783 1,1,-2,2,-3,6,-11,18,-30,56,-105,186,-335,630,-1179,2182,-4080,7710,
%T A320783 -14588,27594,-52377,99858,-190743,364722,-698870,1342176,-2581425,
%U A320783 4971008,-9586395,18512790,-35792449,69273666,-134215680,260300986,-505294125,981706806
%N A320783 Inverse Euler transform of (-1)^(n - 1).
%C A320783 After a(1) and a(2), same as A038063.
%C A320783 The Euler transform of a sequence q is the sequence of coefficients of x^n, n > 0, in the expansion of Product_{n > 0} 1/(1 - x^n)^q(n). The constant term 1 is sometimes taken to be the zeroth part of the Euler transform.
%H A320783 OEIS Wiki, <a href="https://oeis.org/wiki/Euler_transform">Euler transform</a>
%t A320783 EulerInvTransform[{}]={};EulerInvTransform[seq_]:=Module[{final={}},For[i=1,i<=Length[seq],i++,AppendTo[final,i*seq[[i]]-Sum[final[[d]]*seq[[i-d]],{d,i-1}]]];
%t A320783 Table[Sum[MoebiusMu[i/d]*final[[d]],{d,Divisors[i]}]/i,{i,Length[seq]}]];
%t A320783 EulerInvTransform[Array[(-1)^(#-1)&,30]]
%Y A320783 Number theoretical functions: A000005, A000010, A000203, A001055, A001221, A001222, A008683, A010054.
%Y A320783 Euler transforms: A000081, A001970, A006171, A007294, A061255, A061256, A061257, A073576, A117209, A293548, A293549.
%Y A320783 Inverse Euler transforms: A059966, A320767, A320776, A320777, A320778, A320779, A320780, A320781, A320782.
%K A320783 sign
%O A320783 0,3
%A A320783 _Gus Wiseman_, Oct 22 2018