A038071 Shifts left under inverse Euler transform.

1, 1, 0, -1, -1, 0, 1, 0, -1, 0, 2, 1, -3, -3, 4, 7, -4, -14, 3, 28, 4, -53, -30, 91, 95, -142, -240, 191, 556, -165, -1192, -140, 2358, 1215, -4322, -4194, 7211, 11492, -10300, -27839, 10194, 61770, 3506, -127099, -58080, 242071, 218346, -419278

Offset

1,11

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

N. J. A. Sloane, Transforms

Maple

with(numtheory): ietr:= proc(p) local a, c; c:= proc(n) option remember; local j; n*p(n)-add(c(j)*p(n-j), j=1..n-1) end; a:=proc(n) option remember; local d; `if`(n=0, 1, add(mobius(n/d)*c(d), d=divisors(n))/n) end end: aa:= ietr('a'): a:= n-> `if`(n<=1, 1, aa(n-1)): seq(a(n), n=1..48);  # Alois P. Heinz, Sep 08 2008

Mathematica

ietr[p_] := Module[{a, c},
     c[n_] := c[n] = n*p[n] - Sum[c[j]*p[n-j], {j, 1, n-1}];
     a[n_] := a[n] = If[n == 0, 1, Sum[MoebiusMu[n/d]*c[d],
          {d, Divisors[n]}]/n]; a];
aa = ietr[a];
a[n_] := If[n <= 1, 1, aa[n-1]];
Array[a, 48] (* Jean-François Alcover, Mar 01 2021, after Alois P. Heinz *)

Crossrefs

Sequence in context: A207617 A141576 A078019 * A032140 A032044 A321762

Adjacent sequences: A038068 A038069 A038070 * A038072 A038073 A038074

Keyword

sign,eigen

Author

Christian G. Bower, Jan 04 1999

Status

approved