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A127125
Triangle read by rows: T(n,k) is the number of endofunctions on n objects where the multiset of loop sizes forms the k-th partition in Mathematica ordering.
1
1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 4, 3, 3, 1, 2, 1, 1, 1, 1, 1, 1, 9, 6, 6, 3, 6, 3, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 20, 16, 16, 9, 15, 7, 4, 6, 4, 7, 3, 1, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 48, 37, 37, 23, 41, 18, 11, 18, 9, 18, 7, 4, 7, 7, 7, 7, 7, 3, 1, 2, 2, 2, 1, 3, 2, 1, 2, 2, 1, 1, 1
OFFSET
1,5
COMMENTS
The number of loops is equal to the number of components, but the sizes may be smaller.
EXAMPLE
For n = 3, the 7 endofunctions are (1,2,3) -> (1,1,1), (1,1,2), (1,2,1), (2,1,1), (1,2,3), (1,3,2) and (2,3,1). The loops are respectively 1, 1, 1|2, 12, 1|2|3, 1|23 and 123, corresponding to partitions [1], [1], [1^2], [2], [1^3], [2,1] and [3]. The partitions of 1 to 3 in Mathematica order are [1], [2], [1^2], [3], [2,1] and [1^3], so row 3 is 2, 1,1, 1,1,1.
The triangle starts:
1
1, 1 1
2, 1 1, 1 1 1
4, 3 3, 1 2 1, 1 1 1 1 1
CROSSREFS
Sequence in context: A062540 A173636 A115878 * A376799 A256671 A327156
KEYWORD
nonn,tabf
AUTHOR
STATUS
approved