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

0,3

Comments

a(0) = 1 by convention.

Links

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

Formula

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

Example

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.

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 *)

Crossrefs

First differences of A262320.

Sequence in context: A129921 A036670 A369200 * A182995 A027967 A181306

Adjacent sequences: A262318 A262319 A262320 * A262322 A262323 A262324

Keyword

nonn

Author

Alois P. Heinz, Sep 18 2015

Status

approved