|
|
A300335
|
|
Number of ordered set partitions of {1,...,n} with weakly increasing block-sums.
|
|
12
|
|
|
1, 1, 2, 6, 18, 65, 258, 1156, 5558, 29029, 161942, 967921, 6110687, 40807420, 286177944, 2107745450
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
EXAMPLE
|
The a(3) = 6 ordered set partitions: (123), (1)(23), (2)(13), (12)(3), (3)(12), (1)(2)(3).
|
|
MATHEMATICA
|
sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];
Table[Sum[Times@@Factorial/@Length/@GatherBy[sptn, Total], {sptn, sps[Range[n]]}], {n, 8}]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,more
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|