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A325227
Regular triangle read by rows where T(n,k) is the number of integer partitions of n such that the lesser of the maximum part and the number of parts is k.
8
0, 0, 1, 0, 2, 0, 0, 2, 1, 0, 0, 2, 3, 0, 0, 0, 2, 4, 1, 0, 0, 0, 2, 6, 3, 0, 0, 0, 0, 2, 6, 6, 1, 0, 0, 0, 0, 2, 8, 9, 3, 0, 0, 0, 0, 0, 2, 8, 13, 6, 1, 0, 0, 0, 0, 0, 2, 10, 16, 11, 3, 0, 0, 0, 0, 0, 0, 2, 10, 20, 17, 6, 1, 0, 0, 0, 0, 0, 0
OFFSET
1,5
EXAMPLE
Triangle begins:
1
2 0
2 1 0
2 3 0 0
2 4 1 0 0
2 6 3 0 0 0
2 6 6 1 0 0 0
2 8 9 3 0 0 0 0
2 8 13 6 1 0 0 0 0
2 10 16 11 3 0 0 0 0 0
2 10 20 17 6 1 0 0 0 0 0
2 12 24 25 11 3 0 0 0 0 0 0
2 12 28 33 19 6 1 0 0 0 0 0 0
2 14 32 44 29 11 3 0 0 0 0 0 0 0
2 14 38 53 43 19 6 1 0 0 0 0 0 0 0
Row n = 9 counts the following partitions:
(9) (54) (333) (4221) (51111)
(111111111) (63) (432) (4311)
(72) (441) (5211)
(81) (522) (6111)
(22221) (531) (42111)
(222111) (621) (411111)
(2211111) (711)
(21111111) (3222)
(3321)
(32211)
(33111)
(321111)
(3111111)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], Min[Length[#], Max[#]]==k&]], {n, 15}, {k, n}]
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gus Wiseman, Apr 12 2019
STATUS
approved