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

0,2

Links

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

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).

Example

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

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 *)

Crossrefs

Partial sums of A262321.

Cf. A038041, A262280.

Sequence in context: A157748 A046170 A369145 * A062423 A118649 A033482

Adjacent sequences: A262317 A262318 A262319 * A262321 A262322 A262323

Keyword

nonn

Author

Alois P. Heinz, Sep 17 2015

Status

approved