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A256040 Triangle read by rows: number of idempotents of rank k in partition monoid P_n. 0
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 (list; table; graph; refs; listen; history; text; internal format)
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, 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: A209634 A289523 A078220 * A257817 A246710 A139346

Adjacent sequences:  A256037 A256038 A256039 * A256041 A256042 A256043

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane, Mar 14 2015

STATUS

approved

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Last modified March 23 03:57 EDT 2019. Contains 321422 sequences. (Running on oeis4.)