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A320784
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Negated inverse Euler transform of {-1 if n is a triangular number else 0, n > 0} = -A010054.
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1
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1, 1, 0, 1, 1, 1, 2, 3, 3, 5, 8, 11, 14, 23, 31, 47, 68, 101, 144, 217, 315, 471, 693, 1035, 1528, 2287, 3397, 5085, 7587, 11377, 17017, 25565, 38349, 57681, 86724, 130645, 196778, 296853, 447864, 676479, 1022082, 1545685, 2338299, 3540111, 5361606, 8125551
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OFFSET
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0,7
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COMMENTS
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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.
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LINKS
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MATHEMATICA
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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}]]];
Table[Sum[MoebiusMu[i/d]*final[[d]], {d, Divisors[i]}]/i, {i, Length[seq]}]];
-EulerInvTransform[-Table[SquaresR[1, 8*n+1]/2, {n, 30}]]
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CROSSREFS
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Euler transforms: A000081, A001970, A006171, A007294, A061255, A061256, A061257, A073576, A117209, A293548, A293549.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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