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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.)