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A261555
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Triangle read by rows: T(n,k) is number of partitions of n having at least k distinct parts (n >= 1, k >= 1).
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2
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1, 2, 3, 1, 5, 2, 7, 5, 11, 7, 1, 15, 13, 2, 22, 18, 5, 30, 27, 10, 42, 38, 16, 1, 56, 54, 27, 2, 77, 71, 42, 5, 101, 99, 62, 10, 135, 131, 87, 20, 176, 172, 128, 31, 1, 231, 226, 171, 54, 2, 297, 295, 236, 82, 5, 385, 379, 311, 127, 10, 490, 488, 417, 182, 20
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OFFSET
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1,2
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COMMENTS
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Row n has length A003056(n) hence the first element of column k is in row A000217(k).
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REFERENCES
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Jacques Barbot, Essai sur la structuration de l'analyse combinatoire, Paris, Dulac, 1973, Annexe 12A, p. 74.
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LINKS
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FORMULA
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EXAMPLE
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Triangle starts:
1;
2;
3, 1;
5, 2;
7, 5;
11, 7, 1;
15, 13, 2;
22, 18, 5;
30, 27, 10;
42, 38, 16, 1;
56, 54, 27, 2;
77, 71, 42, 5;
...
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MATHEMATICA
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Table[DeleteCases[Map[Count[Map[Length@ Union@ # &, IntegerPartitions@ n], k_ /; k >= #] &, Range@ n], 0], {n, 19}] // Flatten (* Michael De Vlieger, Sep 14 2016 *)
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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