A127121 Number of endofunctions on a set, where the multiset of indegrees forms the n-th partition in Mathematica order (ignoring 0's).

1, 1, 1, 2, 1, 3, 3, 1, 3, 3, 7, 5, 1, 3, 4, 8, 10, 14, 7, 1, 3, 4, 8, 3, 19, 17, 6, 32, 26, 11, 1, 3, 4, 8, 4, 19, 18, 11, 14, 63, 34, 29, 75, 45, 15, 1, 3, 4, 8, 4, 19, 18, 3, 20, 14, 64, 37, 14, 39, 85, 168, 62, 15, 109, 167, 75, 22, 1, 3, 4, 8, 4, 19, 18, 4, 20, 14, 64, 38, 11, 26, 71

Offset

0,4

Comments

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

Links

Table of n, a(n) for n=0..81.

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). In the first, node 1 has indegree 3, the next 3 node 1 has indegree 2 and node 2 has indegree 1 (forming partition [2,1]) and the final 3 are permutations, each node having indegree 1. The partitions of 3 in Mathematica order are [3], [2,1], [1^3], so row 3 of the triangle is 1,3,3.
The triangle starts:
1
1
1 2
1 3 3
1 3 3 7 5
1 3 4 8 10 14 7

Crossrefs

Sequence in context: A309213 A377433 A371103 * A238703 A185908 A234951

Adjacent sequences: A127118 A127119 A127120 * A127122 A127123 A127124

Keyword

nonn,tabf

Author

Franklin T. Adams-Watters, Jan 05 2007

Status

approved