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A058800 = DeleteCasesCases[Import["https://oeis.org/A058800/b058800.txt", "Table"], a_ /; ! MatchQ[a, {_Integer, _Integer, _}]][[All, 2]];
mob[m_, n_] := If[Mod[m, n] == 0, MoebiusMu[m/n], 0];
EULERi[b_List] := Module[{a, c, i, d}, c = {}; For[i = 1, i <= Length[b], i++, c = Append[c, i*b[[i]] - Sum[c[[d]]*b[[i - d]], {d, 1, i - 1}]]]; a = {}; For[i = 1, i <= Length[b], i++, a = Append[a, (1/i)*Sum[mob[i, d]*c[[d]], {d, 1, i}]]]; Return[a]];
(* EulerInvTransform is defined in A022562 *)
EULERiEulerInvTransform[Drop[A058800, 3]] // Rest (* Jean-François Alcover, May 10 2019 , updated Mar 17 2020 *)
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a(1517)-a(1618) (computed from A058800) from Jean-François Alcover, May 10 2019
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1, 2, 6, 25, 116, 625, 3757, 25140, 184511, 1473861, 12711339, 117598686, 1160399052, 12152333659, 134487937252, 1566878426731, 19154490559458
A058800 = DeleteCases[Import["https://oeis.org/A058800/b058800.txt", "Table"], a_ /; ! MatchQ[a, {_Integer, _Integer}]][[All, 2]];
mob[m_, n_] := If[Mod[m, n] == 0, MoebiusMu[m/n], 0];
EULERi[b_List] := Module[{a, c, i, d}, c = {}; For[i = 1, i <= Length[b], i++, c = Append[c, i*b[[i]] - Sum[c[[d]]*b[[i - d]], {d, 1, i - 1}]]]; a = {}; For[i = 1, i <= Length[b], i++, a = Append[a, (1/i)*Sum[mob[i, d]*c[[d]], {d, 1, i}]]]; Return[a]];
EULERi[Drop[A058800, 3]] // Rest (* Jean-François Alcover, May 10 2019 *)
a(15)-a(16) (computed from A058800) from Jean-François Alcover, May 10 2019
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_Christian G. Bower (bowerc(AT)usa.net), _, Dec 28 2000
N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
nonn,hard,new