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A327899
Number of set partitions of {1..n} with equal block sizes and equal block sums.
3
1, 1, 1, 1, 2, 1, 2, 1, 6, 3, 2, 1, 63, 1, 2, 317, 657, 1, 4333, 1, 9609
OFFSET
0,5
EXAMPLE
The a(8) = 6 set partitions:
{{1,2,3,4,5,6,7,8}}
{{1,2,7,8},{3,4,5,6}}
{{1,3,6,8},{2,4,5,7}}
{{1,4,5,8},{2,3,6,7}}
{{1,4,6,7},{2,3,5,8}}
{{1,8},{2,7},{3,6},{4,5}}
MATHEMATICA
sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];
Table[Length[Select[sps[Range[n]], And[SameQ@@Length/@#, SameQ@@Total/@#]&]], {n, 0, 8}]
CROSSREFS
Set partitions with equal block-sizes are A038041.
Set partitions with equal block-sums are A035470.
Sequence in context: A319118 A163820 A284465 * A276157 A169593 A057568
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Sep 29 2019
STATUS
approved