

A127121


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


1



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
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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: A162910 A098975 A309213 * A238703 A185908 A234951
Adjacent sequences: A127118 A127119 A127120 * A127122 A127123 A127124


KEYWORD

nonn,tabf


AUTHOR

Franklin T. AdamsWatters, Jan 05 2007


STATUS

approved



