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

Author

Franklin T. Adams-Watters, Jan 05 2007

Keywords

• nonn
• tabf

Comments

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

Examples

			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