A034743 a(n) = Sum_{d | n} mu(n/d) * Bell(d-1).

1, 0, 1, 4, 14, 50, 202, 872, 4138, 21132, 115974, 678514, 4213596, 27644234, 190899306, 1382957668, 10480142146, 82864865614, 682076806158, 5832742183906, 51724158235168, 474869816040776, 4506715738447322

Offset: 1

Author

Erich Friedman

Keywords

• nonn

Comments

A kind of Dirichlet convolution of mu(n) with Bell numbers.

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A000110, A008683, A082951.

Programs

Mathematica

a[n_] := Sum[MoebiusMu[n/d]*BellB[d - 1], {d, Divisors[n]}];
Array[a, 23] (* Jean-François Alcover, Sep 08 2019 *)

PARI

bell(n) = sum(k=0,n,stirling(n,k,2));
a(n) = sumdiv(n,d, moebius(n/d) * bell(d-1)); \\ Andrew Howroyd, Apr 03 2017

Extensions

More precise definition from Andrew Howroyd, Apr 03 2017