A327899 - OEIS

A327899

Number of set partitions of {1..n} with equal block sizes and equal block sums.

1, 1, 1, 1, 2, 1, 2, 1, 6, 3, 2, 1, 63, 1, 2, 317, 657, 1, 4333, 1, 9609

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OFFSET

0,5

LINKS

EXAMPLE

The a(8) = 6 set partitions:

{{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.

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Sep 29 2019

STATUS

approved