OFFSET
0,10
COMMENTS
The number of submultisets of a partition is the product of its multiplicities, each plus one.
LINKS
Alois P. Heinz, Rows n = 0..60, flattened
FORMULA
EXAMPLE
Triangle begins:
1
0 1
0 1 1
0 1 0 2
0 1 1 1 1 1
0 1 0 2 0 3 0 1
0 1 1 3 0 1 1 2 1 1
0 1 0 3 0 3 0 4 0 1 0 3
0 1 1 3 1 3 0 3 2 1 0 4 0 1 1 1
0 1 0 5 0 3 0 5 0 3 0 6 0 1 0 3 0 2 0 1
0 1 1 4 0 5 0 7 2 1 1 4 0 1 2 5 0 3 0 2 1 0 0 2
Row n = 7 counts the following partitions (empty columns not shown):
(7) (43) (322) (421) (31111) (3211)
(52) (331) (2221) (22111)
(61) (511) (4111) (211111)
(1111111)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], Times@@(1+Length/@Split[#])==k&]], {n, 0, 10}, {k, 1, Max@@(Times@@(1+Length/@Split[#])&)/@IntegerPartitions[n]}]
CROSSREFS
KEYWORD
AUTHOR
Gus Wiseman, May 30 2019
STATUS
approved