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A120774 Number of ordered set partitions of [n] where equal-sized blocks are ordered with increasing least elements. 6
1, 1, 2, 8, 31, 147, 899, 5777, 41024, 322488, 2749325, 25118777, 245389896, 2554780438, 28009868787, 323746545433, 3933023224691, 49924332801387, 661988844566017, 9138403573970063, 131043199040556235, 1949750421507432009, 30031656711776544610 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Old name was: Row sums of A179233.

a(n) is the number of ways to linearly order the blocks in each set partition of {1,2,...,n} where two blocks are considered identical if they have the same number of elements. - Geoffrey Critzer, Sep 29 2011

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..525

EXAMPLE

A179233 begins 1; 1; 1 1; 6 1 1; 8 3 18 1 1 ... with row sums 1, 1 2 8 31 147 ...

a(3) = 8: 123, 1|23, 23|1, 2|13, 13|2, 3|12, 12|3, 1|2|3. - Alois P. Heinz, Apr 27 2017

MAPLE

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

      (p+n)!/n!, add(b(n-i*j, i-1, p+j)*combinat

      [multinomial](n, n-i*j, i$j)/j!^2, j=0..n/i))

    end:

a:= n-> b(n$2, 0):

seq(a(n), n=0..25);  # Alois P. Heinz, Apr 27 2017

MATHEMATICA

f[{x_, y_}]:= x!^y y!;   Table[Total[Table[n!, {PartitionsP[n]}]/Apply[Times, Map[f, Map[Tally, Partitions[n]], {2}], 2] * Apply[Multinomial, Map[Last, Map[Tally, Partitions[n]], {2}], 2]], {n, 0, 20}]  (* Geoffrey Critzer, Sep 29 2011 *)

CROSSREFS

Cf. A000041, A032011, A049019, A096161, A096162, A196301.

Row sums of A179233, A285824.

Main diagonal of A327244.

Sequence in context: A150827 A150828 A308336 * A261052 A128324 A264572

Adjacent sequences:  A120771 A120772 A120773 * A120775 A120776 A120777

KEYWORD

easy,nonn

AUTHOR

Alford Arnold, Jul 12 2006

EXTENSIONS

Leading 1 inserted, definition simplified by R. J. Mathar, Sep 28 2011

a(15) corrected, more terms, and new name (using Geoffrey Critzer's comment) from Alois P. Heinz, Apr 27 2017

STATUS

approved

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Last modified February 22 18:03 EST 2020. Contains 332148 sequences. (Running on oeis4.)