A256040 Triangle read by rows: number of idempotents of rank k in partition monoid P_n.

1, 1, 1, 4, 7, 1, 25, 70, 18, 1, 225, 921, 331, 34, 1, 2704, 15191, 6880, 995, 55, 1, 41209, 304442, 163336, 29840, 2345, 81, 1, 769129, 7240353, 4411190, 958216, 95760, 4739, 112, 1, 17139600, 200542851, 134522725, 33395418, 3992891, 252770, 8610, 148, 1, 447195609, 6372361738, 4595689200, 1267427533, 174351471, 13274751, 581196, 14466, 189, 1

Offset

0,4

Links

Table of n, a(n) for n=0..54.

I. Dolinka, J. East, A. Evangelou, D. FitzGerald, N. Ham, et al., Enumeration of idempotents in diagram semigroups and algebras, arXiv preprint arXiv:1408.2021 [math.GR], 2014.

Example

Triangle begins:
1,
1, 1,
4, 7, 1,
25, 70, 18, 1,
225, 921, 331, 34, 1,
2704, 15191, 6880, 995, 55, 1,
41209, 304442, 163336, 29840, 2345, 81, 1,
769129, 7240353, 4411190, 958216, 95760, 4739, 112, 1,
17139600, 200542851, 134522725, 33395418, 3992891, 252770, 8610, 148, 1,
...

Crossrefs

Sequence in context: A340584 A289523 A078220 * A363746 A257817 A246710

Adjacent sequences: A256037 A256038 A256039 * A256041 A256042 A256043

Keyword

nonn,tabl

Author

N. J. A. Sloane, Mar 14 2015

Status

approved