A127124 Number of endofunctions whose component sizes form the n-th partition in Mathematica order.

1, 1, 2, 1, 4, 2, 1, 9, 4, 3, 2, 1, 20, 9, 8, 4, 3, 2, 1, 51, 20, 18, 9, 10, 8, 4, 4, 3, 2, 1, 125, 51, 40, 20, 36, 18, 9, 10, 12, 8, 4, 4, 3, 2, 1, 329, 125, 102, 51, 80, 40, 20, 45, 36, 27, 18, 9, 20, 10, 12, 8, 4, 5, 4, 3, 2, 1, 862, 329, 250, 125, 204, 102, 51, 180, 80, 60, 40, 20, 45

Offset

0,3

Comments

Can be regarded as a triangle with one row for each size of partition.

Links

Table of n, a(n) for n=0..79.

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 components are respectively 123, 123, 13|2, 123, 1|2|3, 1|23 and 123, corresponding to partitions [3], [3], [2,1], [3], [1^3], [2,1] and [3]. The partitions of 3 in Mathematica order are [3], [2,1] and [1^3], so row 3 is 4,2,1.
The triangle starts:
1
1
2 1
4 2 1
9 4 3 2 1
20 9 8 4 3 2 1

Crossrefs

Sequence in context: A274106 A354802 A158982 * A127136 A239101 A362266

Adjacent sequences: A127121 A127122 A127123 * A127125 A127126 A127127

Keyword

nonn,tabf

Author

Franklin T. Adams-Watters, Jan 05 2007

Status

approved