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 A325242 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. 29
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS For example, the partition (32111) has multiplicities {1,1,3}, of which 2 are distinct, so is counted under T(8,2). LINKS Alois P. Heinz, Rows n = 1..200, flattened EXAMPLE 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) MATHEMATICA DeleteCases[Table[Length[Select[IntegerPartitions[n], Length[Union[Length/@Split[#]]]==k&]], {n, 20}, {k, n}], 0, 2] CROSSREFS 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: A003324 A110630 A238883 * A257053 A129717 A317088 Adjacent sequences:  A325239 A325240 A325241 * A325243 A325244 A325245 KEYWORD nonn,tabf AUTHOR Gus Wiseman, Apr 15 2019 STATUS approved

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Last modified August 18 08:57 EDT 2019. Contains 326077 sequences. (Running on oeis4.)