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A300335
Number of ordered set partitions of {1,...,n} with weakly increasing block-sums.
13
1, 1, 2, 6, 18, 65, 258, 1156, 5558, 29029, 161942, 967921, 6110687, 40807420, 286177944, 2107745450, 16202590638, 130043111849, 1085011337141, 9408577992091, 84501248359552, 786018565954838, 7550153439748394
OFFSET
0,3
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
Gus Wiseman, Mar 03 2018
EXTENSIONS
a(12)-a(15) from Alois P. Heinz, Mar 03 2018
a(16)-a(22) from Christian Sievers, Aug 30 2024
STATUS
approved