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

0,3

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

Formula

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

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 *)

Crossrefs

Cf. A004111, A196154, A196161.

Sequence in context: A178833 A212657 A065955 * A104880 A152478 A102973

Adjacent sequences: A196115 A196116 A196117 * A196119 A196120 A196121

Keyword

nonn

Author

N. J. A. Sloane, Oct 27 2011

Status

approved