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A297924 Number of set partitions of [2n] in which the size of the last block is n. 5
1, 1, 4, 20, 125, 952, 8494, 86025, 969862, 12020580, 162203607, 2363458396, 36930606254, 615302885459, 10878670826170, 203268056115256, 3999642836434361, 82617423216826640, 1786559190116778030, 40344863179696283037, 949348461372003462390 (list; graph; refs; listen; history; text; internal format)
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..466

Wikipedia, Partition of a set

FORMULA

a(n) = A121207(2n,n) = A124496(2n,n).

EXAMPLE

a(1) = 1: 1|2.

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

a(3) = 20: 123|456, 124|356, 125|346, 126|345, 12|3|456, 134|256, 135|246, 136|245, 13|2|456, 145|236, 146|235, 156|234, 1|23|456, 14|2|356, 1|24|356, 15|2|346, 1|25|346, 16|2|345, 1|26|345, 1|2|3|456.

MAPLE

b:= proc(n, k) option remember; `if`(n=k, 1,

      add(b(n-j, k)*binomial(n-1, j-1), j=1..n-k))

    end:

a:= n-> b(2*n, n):

seq(a(n), n=0..25);

MATHEMATICA

b[n_, k_] := b[n, k] = If[n == k, 1, Sum[b[n - j, k]*Binomial[n - 1, j - 1], {j, 1, n - k}]];

a[n_] := b[2*n, n];

Table[a[n], {n, 0, 25}] (* Jean-Fran├žois Alcover, May 20 2018, translated from Maple *)

CROSSREFS

Cf. A121207, A124496, A276961, A297926.

Sequence in context: A067121 A002793 A162509 * A151341 A285868 A266490

Adjacent sequences:  A297921 A297922 A297923 * A297925 A297926 A297927

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jan 08 2018

STATUS

approved

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Last modified May 12 11:51 EDT 2021. Contains 343821 sequences. (Running on oeis4.)