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A325194
Regular triangle read by rows where T(n,k) is the number of integer partitions of n with co-rank n - k, where co-rank is the greater of the length and the largest part.
3
1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 3, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 5, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 7, 1, 0, 0, 0
OFFSET
0,13
EXAMPLE
Triangle begins:
1
0 0
0 1 0
0 0 0 0
0 0 2 0 0
0 0 0 1 0 0
0 0 0 2 1 0 0
0 0 0 0 2 0 0 0
0 0 0 0 2 3 0 0 0
0 0 0 0 0 2 3 0 0 0
0 0 0 0 0 2 4 2 0 0 0
0 0 0 0 0 0 2 5 1 0 0 0
0 0 0 0 0 0 2 4 7 1 0 0 0
0 0 0 0 0 0 0 2 6 6 0 0 0 0
0 0 0 0 0 0 0 2 4 9 7 0 0 0 0
0 0 0 0 0 0 0 0 2 6 11 5 0 0 0 0
0 0 0 0 0 0 0 0 2 4 10 14 5 0 0 0 0
0 0 0 0 0 0 0 0 0 2 6 13 15 3 0 0 0 0
0 0 0 0 0 0 0 0 0 2 4 10 19 17 2 0 0 0 0
0 0 0 0 0 0 0 0 0 0 2 6 14 22 17 1 0 0 0 0
0 0 0 0 0 0 0 0 0 0 2 4 10 21 29 17 1 0 0 0 0
Row n = 16 counts the following partitions:
(8) (72) (64) (533) (444)
(11111111) (711) (622) (542) (3333)
(2211111) (631) (551) (4332)
(3111111) (6211) (5222) (4422)
(61111) (5321) (4431)
(222211) (5411)
(322111) (32222)
(331111) (33221)
(421111) (33311)
(511111) (42221)
(43211)
(44111)
(52211)
(53111)
MATHEMATICA
Table[Length[Select[IntegerPartitions[k], Max[Length[#], Max[#]]==n-k&]], {n, 0, 10}, {k, 0, n}]
CROSSREFS
Column sums are A000041. Row sums are A325193.
Sequence in context: A326075 A060862 A325801 * A066087 A294927 A080224
KEYWORD
nonn,tabl
AUTHOR
Gus Wiseman, Apr 13 2019
STATUS
approved