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A320438
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Irregular triangle read by rows where T(n,d) is the number of set partitions of {1,...n} with all block-sums equal to d, where d is a divisor of 1 + ... + n.
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0
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 3, 7, 1, 1, 9, 1, 1, 1, 1, 43, 35, 1, 1, 102, 62, 1, 1, 1, 1, 68, 595, 1, 1, 17, 187, 871, 1480, 361, 1, 1, 2650, 657, 1, 1, 9294, 1, 1, 23728, 1
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OFFSET
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1,12
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LINKS
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EXAMPLE
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Triangle begins:
1
1
1 1
1 1
1 1
1 1
1 4 1
1 3 7 1
1 9 1
1 1
1 43 35 1
1 102 62 1
1 1
1 68 595 1
1 17 187 871 1480 361 1
1 2650 657 1
Row 8 counts the following set partitions:
{{18}{27}{36}{45}} {{1236}{48}{57}} {{12348}{567}} {{12345678}}
{{138}{246}{57}} {{12357}{468}}
{{156}{237}{48}} {{12456}{378}}
{{1278}{3456}}
{{1368}{2457}}
{{1458}{2367}}
{{1467}{2358}}
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MATHEMATICA
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spsu[_, {}]:={{}}; spsu[foo_, set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@spsu[Select[foo, Complement[#, Complement[set, s]]=={}&], Complement[set, s]]]/@Cases[foo, {i, ___}];
Table[Length[spsu[Select[Subsets[Range[n]], Total[#]==d&], Range[n]]], {n, 12}, {d, Select[Divisors[n*(n+1)/2], #>=n&]}]
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CROSSREFS
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Cf. A000110, A000258, A008277, A112956, A164977, A275714, A279375, A300335, A320423, A320424, A321455, A321469.
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KEYWORD
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nonn,tabf,more
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AUTHOR
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STATUS
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approved
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