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A325242
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Irregular triangle read by rows with zeros removed where T(n,k) is the number of integer partitions of n with k distinct multiplicities, n > 0.
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32
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1, 2, 3, 4, 1, 4, 3, 8, 3, 6, 9, 10, 12, 11, 19, 15, 26, 1, 13, 39, 4, 25, 47, 5, 19, 70, 12, 29, 89, 17, 33, 115, 28, 42, 148, 41, 39, 189, 69, 62, 235, 88, 55, 294, 141, 81, 362, 183, 1, 84, 450, 253, 5, 103, 558, 333, 8, 105, 669, 464, 17, 153, 817, 576, 29
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OFFSET
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1,2
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COMMENTS
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For example, the partition (32111) has multiplicities {1,1,3}, of which 2 are distinct, so is counted under T(8,2).
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LINKS
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Alois P. Heinz, Rows n = 1..200, flattened
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EXAMPLE
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Triangle begins:
1
2
3
4 1
4 3
8 3
6 9
10 12
11 19
15 26 1
13 39 4
25 47 5
19 70 12
29 89 17
33 115 28
42 148 41
39 189 69
62 235 88
55 294 141
81 362 183 1
Row n = 8 counts the following partitions:
(8) (332)
(44) (422)
(53) (611)
(62) (3221)
(71) (4211)
(431) (5111)
(521) (22211)
(2222) (32111)
(3311) (41111)
(11111111) (221111)
(311111)
(2111111)
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MATHEMATICA
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DeleteCases[Table[Length[Select[IntegerPartitions[n], Length[Union[Length/@Split[#]]]==k&]], {n, 20}, {k, n}], 0, 2]
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CROSSREFS
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Row lengths are A056556. Row sums are A000041. Column k = 1 is A047966. Column k = 2 is A325243.
Cf. A008284, A062770, A071625, A098859, A116608, A127002, A183558, A243978, A244515, A325244, A325268.
Sequence in context: A110630 A343321 A238883 * A257053 A129717 A317088
Adjacent sequences: A325239 A325240 A325241 * A325243 A325244 A325245
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KEYWORD
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nonn,tabf
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AUTHOR
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Gus Wiseman, Apr 15 2019
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STATUS
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approved
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