A262280 Number of ways to select a nonempty subset s from an n-set and then partition s into blocks of equal size.

0, 1, 4, 11, 29, 72, 190, 527, 1552, 5031, 18087, 66904, 266381, 1164516, 5215644, 23868103, 117740143, 609872350, 3268548406, 18110463455, 102867877414, 620476915965, 4005216028161, 25747549921338, 166978155172420, 1168774024335203, 8556355097320141

Offset: 0

Author

Alois P. Heinz, Sep 17 2015

Keywords

• nonn

Examples

			a(3) = 11: 1, 2, 3, 12, 1|2, 13, 1|3, 23, 2|3, 123, 1|2|3.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..616

Crossrefs

Cf. A038041, A262320.

Programs

Maple

b:= proc(n) option remember;
      add(1/(d!*(n/d)!^d), d=numtheory[divisors](n))
    end:
a:= n-> n! * add(b(k)/(n-k)!, k=1..n):
seq(a(n), n=0..30);

Mathematica

b[n_] := b[n] = DivisorSum[n, 1/(#!*(n/#)!^#)&]; a[n_] := n!*Sum[b[k]/(n-k)!, {k, 1, n}]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Feb 15 2017, translated from Maple *)

Formula

E.g.f.: exp(x) * Sum_{k>=1} (exp(x^k/k!)-1).

a(n) = Sum_{k=1..n} C(n,k) * A038041(k).

a(n) = A262320(n) - 1.