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A275282 Number of set partitions of [n] with symmetric block size list. 2
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, May 27 2018, from Maple *)

CROSSREFS

Row sums of A275281.

Sequence in context: A267214 A107386 A095021 * A101372 A133374 A267446

Adjacent sequences:  A275279 A275280 A275281 * A275283 A275284 A275285

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jul 21 2016

STATUS

approved

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Last modified February 17 18:46 EST 2019. Contains 320222 sequences. (Running on oeis4.)