A057772 Inverse Euler transform of A000016.

1, 0, 1, 0, 2, 1, 4, 4, 12, 15, 34, 55, 110, 190, 370, 664, 1272, 2350, 4466, 8372, 15926, 30105, 57390, 109202, 208738, 398985, 764906, 1467370, 2820770, 5427543, 10459456, 20176561, 38969684, 75339232, 145804978, 282429242, 547573768, 1062501151, 2063317650

Offset

1,5

References

P. J. Cameron, Some counting problems related to permutation groups, Discrete Math., 225 (2000), 77-92.

Links

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

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: a:= ietr(n-> add(phi(d) *2^(n/d)/2/n, d=select(m-> modp(m, 2)=1, divisors(n)))): seq(a(n), n=1..40); # Alois P. Heinz, Sep 08 2008
# The function EulerInvTransform is defined in A358451.
a := EulerInvTransform(A000016):
seq(a(n), n = 1..39); # Peter Luschny, Nov 21 2022

Mathematica

ietr[p_] := Module[{a, c}, c[n_] := c[n] = Module[{j}, n*p[n] - Sum[c[j]*p[n-j], {j, 1, n-1}]]; a[n_] := a[n] = Module[{d}, If[n == 0, 1, Sum[MoebiusMu[n/d]*c[d], {d, Divisors[n]}]/n]]; a]; a = ietr[Function[n, Sum[EulerPhi[d]*2^(n/d)/2/n, {d, Select[Divisors[n], OddQ]}]]]; Table[a[n], {n, 1, 40}] (* Jean-François Alcover, Jan 17 2014, after Alois P. Heinz *)

Crossrefs

Sequence in context: A211178 A048049 A212716 * A145861 A191660 A129874

Adjacent sequences: A057769 A057770 A057771 * A057773 A057774 A057775

Keyword

nonn

Author

N. J. A. Sloane, Nov 02 2000

Extensions

Better definition and more terms from Vladeta Jovovic, Mar 13 2008

Status

approved