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 A320782 Inverse Euler transform of the unsigned Moebius function A008966. 7
 1, 1, 0, 0, -1, 1, 0, 0, -1, 1, 0, 0, -2, 3, 0, -1, -3, 6, -3, 0, -6, 12, -6, 0, -9, 23, -17, 0, -15, 47, -40, 8, -24, 91, -101, 34, -46, 181, -230, 109, -92, 354, -534, 323, -208, 690, -1177, 883, -520, 1365, -2603, 2297, -1377, 2760, -5641, 5789, -3721, 5741 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,13 COMMENTS 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. LINKS Table of n, a(n) for n=0..57. OEIS Wiki, Euler transform MATHEMATICA 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[Abs[MoebiusMu[n]], {n, 30}]] CROSSREFS Number theoretical functions: A000005, A000010, A000203, A001055, A001221, A001222, A008683, A010054. Euler transforms: A000081, A001970, A006171, A007294, A061255, A061256, A061257, A073576, A117209, A293548, A293549. Inverse Euler transforms: A059966, A320767, A320776, A320777, A320778, A320779, A320780, A320781. Sequence in context: A195467 A112168 A072516 * A191588 A106450 A255961 Adjacent sequences: A320779 A320780 A320781 * A320783 A320784 A320785 KEYWORD sign AUTHOR Gus Wiseman, Oct 22 2018 STATUS approved

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Last modified February 21 03:52 EST 2024. Contains 370219 sequences. (Running on oeis4.)