|
|
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
|
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
|
|
|
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):
|
|
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
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
Leading 1 inserted, definition simplified by R. J. Mathar, Sep 28 2011
|
|
STATUS
|
approved
|
|
|
|