A276961 Number of set partitions of [2n] with largest set of size n.

1, 1, 9, 90, 1015, 12978, 187110, 3008148, 53275365, 1028142830, 21426984722, 478684639524, 11394222257054, 287518726261900, 7658231720886900, 214521099685649640, 6299407928673657135, 193373975592937777770, 6189939300880260745050, 206159811915115686404700

Offset

0,3

Comments

The blocks are ordered with increasing least elements.

a(0) = 1 by convention.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..445

Wikipedia, Partition of a set

Formula

a(n) = A080510(2n,n).

a(n) = A327884(2n,n).

a(n) = ceiling(C(2n,n)*(A000110(n)-1/2)). - Ludovic Schwob, Jan 15 2022

Example

a(1) = 1: 1|2.
a(2) = 9: 12|34, 12|3|4, 13|24, 13|2|4, 14|23, 1|23|4, 14|2|3, 1|24|3, 1|2|34.

Maple

b:= proc(n, k) option remember; `if`(n=0, 1, add(
      b(n-i, k)*binomial(n-1, i-1), i=1..min(n, k)))
    end:
a:= n-> `if`(n=0, 1, b(2*n, n)-b(2*n, n-1)):
seq(a(n), n=0..20);

Mathematica

b[n_, k_] := b[n, k] = If[n == 0, 1, Sum[b[n - i, k]*Binomial[n - 1, i - 1], {i, 1, Min[n, k]}]];
a[n_] := If[n == 0, 1, b[2*n, n] - b[2*n, n - 1]];
Table[a[n], {n, 0, 20}] (* Jean-François Alcover, May 20 2018, translated from Maple *)

Crossrefs

Cf. A000110, A080510, A276923, A297924, A297926, A327884, A328156.

Sequence in context: A276506 A049389 A127769 * A062815 A294610 A294813

Adjacent sequences: A276958 A276959 A276960 * A276962 A276963 A276964

Keyword

nonn

Author

Alois P. Heinz, Sep 22 2016

Status

approved