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%I #4 Oct 22 2018 22:55:20
%S 1,1,0,1,1,1,2,3,3,5,8,11,14,23,31,47,68,101,144,217,315,471,693,1035,
%T 1528,2287,3397,5085,7587,11377,17017,25565,38349,57681,86724,130645,
%U 196778,296853,447864,676479,1022082,1545685,2338299,3540111,5361606,8125551
%N Negated inverse Euler transform of {-1 if n is a triangular number else 0, n > 0} = -A010054.
%C 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 OEIS Wiki, <a href="https://oeis.org/wiki/Euler_transform">Euler transform</a>
%t 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 Table[Sum[MoebiusMu[i/d]*final[[d]],{d,Divisors[i]}]/i,{i,Length[seq]}]];
%t -EulerInvTransform[-Table[SquaresR[1,8*n+1]/2,{n,30}]]
%Y Number theoretical functions: A000005, A000010, A000203, A001055, A001221, A001222, A008683, A010054.
%Y Euler transforms: A000081, A001970, A006171, A007294, A061255, A061256, A061257, A073576, A117209, A293548, A293549.
%Y Inverse Euler transforms: A059966, A320767, A320776, A320777, A320778, A320779, A320780, A320781, A320782.
%K nonn
%O 0,7
%A _Gus Wiseman_, Oct 22 2018