A196118 Partial sums of A004111.

0, 1, 2, 3, 5, 8, 14, 26, 51, 103, 216, 463, 1011, 2237, 5007, 11306, 25732, 58941, 135792, 314410, 731258, 1707554, 4001778, 9409162, 22189556, 52472676, 124397323, 295594279, 703904947, 1679567427, 4015010504, 9614519152, 23060649590, 55395487476

Offset: 0

Author

N. J. A. Sloane, Oct 27 2011

Keywords

• nonn

Comments

A004111 is an important sequence and the OEIS should include various sequences derived from it.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A004111, A196154, A196161.

Programs

Maple

with(numtheory):
b:= proc(n) option remember; `if`(n<2, n, add(b(n-k)*add(
      b(d)*d*(-1)^(k/d+1), d=divisors(k)), k=1..n-1)/(n-1))
    end:
a:= proc(n) option remember; b(n)+`if`(n>0, a(n-1), 0) end:
seq(a(n), n=0..50);  # Alois P. Heinz, Feb 24 2015

Mathematica

b[n_] := b[n] = If[n<2, n, Sum[b[n-k]*Sum[b[d]*d*(-1)^(k/d+1), {d, Divisors[k]}], {k, 1, n-1}]/(n-1)]; a[n_] := a[n] = b[n] + If[n>0, a[n-1], 0]; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Feb 17 2016, after Alois P. Heinz *)

Formula

a(n) ~ c * A246169^n / n^(3/2), where c = 0.601433809400132103408618319570970615307211984303335915895942080355184647... - Vaclav Kotesovec, Dec 26 2020