A262321 Number of ways to select a subset s containing n from {1,...,n} and then partition s into blocks of equal size.

1, 1, 3, 7, 18, 43, 118, 337, 1025, 3479, 13056, 48817, 199477, 898135, 4051128, 18652459, 93872040, 492132207, 2658676056, 14841915049, 84757413959, 517609038551, 3384739112196, 21742333893177, 141230605251082, 1001795869162783, 7387581072984938

Offset: 0

Author

Alois P. Heinz, Sep 18 2015

Keywords

• nonn

Comments

a(0) = 1 by convention.

Examples

			a(0) = 1: {}.
a(1) = 1: 1.
a(2) = 3: 2, 12, 1|2.
a(3) = 7: 3, 13, 1|3, 23, 2|3, 123, 1|2|3.
a(4) = 18: 4, 14, 1|4, 24, 2|4, 34, 3|4, 124, 1|2|4, 134, 1|3|4, 234, 2|3|4, 1234, 12|34, 13|24, 14|23, 1|2|3|4.
		

Links

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

Crossrefs

First differences of A262320.

Programs

Maple

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

Mathematica

b[n_] := b[n] = n!*If[n == 0, 1, DivisorSum[n, 1/(#!*(n/#)!^#)&]];
a[n_] :=  Sum[b[k]*Binomial[n-1, k-1], {k, 0, n}];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Mar 28 2017, translated from Maple *)

Formula

E.g.f.: A(x) - Integral_{x} A(x) dx, with A(x) = e.g.f. of A262320.