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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

The number of loops is equal to the number of components, but the sizes may be smaller.

LINKS

Table of n, a(n) for n=1..99.

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 * A256671 A327156 A114171

Adjacent sequences:  A127122 A127123 A127124 * A127126 A127127 A127128

KEYWORD

nonn,tabf

AUTHOR

Franklin T. Adams-Watters, Jan 05 2007

STATUS

approved

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Last modified June 6 18:59 EDT 2020. Contains 334832 sequences. (Running on oeis4.)