A275282 Number of set partitions of [n] with symmetric block size list.

1, 1, 2, 2, 7, 9, 47, 80, 492, 985, 7197, 16430, 139316, 361737, 3425683, 9939134, 103484333, 329541459, 3747921857, 12980700318, 159811532315, 598410986533, 7902918548186, 31781977111506, 447462660895105, 1920559118957107, 28699615818386524, 130838216971937408

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..400

Wikipedia, Partition of a set

Formula

a(n) = Sum_{k=0..n} A275281(n,k).

Example

a(3) = 2: 123, 1|2|3.
a(4) = 7: 1234, 12|34, 13|24, 14|23, 1|23|4, 1|24|3, 1|2|3|4.
a(5) = 9: 12345, 12|3|45, 13|2|45, 1|234|5, 1|235|4, 14|2|35, 1|245|3, 15|2|34, 1|2|3|4|5.

Maple

b:= proc(n, s) option remember; `if`(n>s,
      binomial(n-1, n-s-1), 1) +add(binomial(n-1, j-1)*
      b(n-j, s+j) *binomial(s+j-1, j-1), j=1..(n-s)/2)
    end:
a:= n-> b(n, 0):
seq(a(n), n=0..30);

Mathematica

b[n_, s_] := b[n, s] = If[n > s, Binomial[n-1, n-s-1], 1] + Sum[Binomial[n - 1, j - 1]*b[n - j, s + j]*Binomial[s + j - 1, j - 1], {j, 1, (n-s)/2}];
a[n_] := b[n, 0];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, May 27 2018, from Maple *)

Crossrefs

Row sums of A275281.

Sequence in context: A095021 A347913 A348532 * A307633 A101372 A133374

Adjacent sequences: A275279 A275280 A275281 * A275283 A275284 A275285

Keyword

nonn

Author

Alois P. Heinz, Jul 21 2016

Status

approved