cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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.

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%I A325242 #10 Apr 16 2019 18:32:10
%S A325242 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,
%T A325242 29,89,17,33,115,28,42,148,41,39,189,69,62,235,88,55,294,141,81,362,
%U A325242 183,1,84,450,253,5,103,558,333,8,105,669,464,17,153,817,576,29
%N 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.
%C A325242 For example, the partition (32111) has multiplicities {1,1,3}, of which 2 are distinct, so is counted under T(8,2).
%H A325242 Alois P. Heinz, <a href="/A325242/b325242.txt">Rows n = 1..200, flattened</a>
%e A325242 Triangle begins:
%e A325242    1
%e A325242    2
%e A325242    3
%e A325242    4   1
%e A325242    4   3
%e A325242    8   3
%e A325242    6   9
%e A325242   10  12
%e A325242   11  19
%e A325242   15  26   1
%e A325242   13  39   4
%e A325242   25  47   5
%e A325242   19  70  12
%e A325242   29  89  17
%e A325242   33 115  28
%e A325242   42 148  41
%e A325242   39 189  69
%e A325242   62 235  88
%e A325242   55 294 141
%e A325242   81 362 183   1
%e A325242 Row n = 8 counts the following partitions:
%e A325242   (8)         (332)
%e A325242   (44)        (422)
%e A325242   (53)        (611)
%e A325242   (62)        (3221)
%e A325242   (71)        (4211)
%e A325242   (431)       (5111)
%e A325242   (521)       (22211)
%e A325242   (2222)      (32111)
%e A325242   (3311)      (41111)
%e A325242   (11111111)  (221111)
%e A325242               (311111)
%e A325242               (2111111)
%t A325242 DeleteCases[Table[Length[Select[IntegerPartitions[n],Length[Union[Length/@Split[#]]]==k&]],{n,20},{k,n}],0,2]
%Y A325242 Row lengths are A056556. Row sums are A000041. Column k = 1 is A047966. Column k = 2 is A325243.
%Y A325242 Cf. A008284, A062770, A071625, A098859, A116608, A127002, A183558, A243978, A244515, A325244, A325268.
%K A325242 nonn,tabf
%O A325242 1,2
%A A325242 _Gus Wiseman_, Apr 15 2019