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A297926 Number of set partitions of [2n] in which the size of the first block is n. 5
1, 1, 6, 50, 525, 6552, 93786, 1504932, 26640900, 514083570, 10713538550, 239342496120, 5697111804566, 143759365731100, 3829115870472600, 107260549881604200, 3149703964487098665, 96686987797052290440, 3094969650442399156350, 103079905957566679518300 (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..445

Wikipedia, Partition of a set

FORMULA

a(n) = binomial(2*n-1,n-1) * Bell(n).

a(n) = A056857(2n,n) = A056860(2n,n).

EXAMPLE

a(1) = 1: 1|2.

a(2) = 6: 12|34, 12|3|4, 13|24, 13|2|4, 14|23, 14|2|3.

MAPLE

b:= proc(n) option remember; `if`(n=0, 1,

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

    end:

a:= n-> binomial(2*n-1, n-1)*b(n):

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

MATHEMATICA

b[n_] := b[n] = If[n == 0, 1, Sum[b[n-j]*Binomial[n-1, j-1], {j, 1, n}]];

a[n_] := Binomial[2*n-1, n-1] * b[n];

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

CROSSREFS

Cf. A000110, A056857, A056860, A276961, A297924.

Sequence in context: A005416 A300989 A105617 * A094072 A058784 A008380

Adjacent sequences:  A297923 A297924 A297925 * A297927 A297928 A297929

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jan 08 2018

STATUS

approved

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Last modified January 20 11:11 EST 2020. Contains 331083 sequences. (Running on oeis4.)