A262320 Number of ways to select a subset s from an n-set and then partition s into blocks of equal size.

1, 2, 5, 12, 30, 73, 191, 528, 1553, 5032, 18088, 66905, 266382, 1164517, 5215645, 23868104, 117740144, 609872351, 3268548407, 18110463456, 102867877415, 620476915966, 4005216028162, 25747549921339, 166978155172421, 1168774024335204, 8556355097320142

Offset: 0

Author

Alois P. Heinz, Sep 17 2015

Keywords

• nonn

Examples

			a(3) = 12: {}, 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

Partial sums of A262321.

Cf. A038041, A262280.

Programs

Maple

b:= proc(n) option remember;
      add(1/(d!*(n/d)!^d), d=numtheory[divisors](n))
    end:
a:= n-> 1 + 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_] := 1 + n! * Sum[b[k]/(n-k)!, {k, 1, n}]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Dec 18 2016, after Alois P. Heinz *)

Formula

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

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

a(n) = 1 + A262280(n).

a(n) = Sum_{k=0..n} A262321(k).