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A256037
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Triangle read by rows: number of R-class idempotents of rank k in Brauer monoid B_n.
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0
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1, 0, 1, 1, 0, 1, 0, 3, 0, 1, 3, 0, 5, 0, 1, 0, 15, 0, 7, 0, 1, 15, 0, 35, 0, 9, 0, 1, 0, 105, 0, 63, 0, 11, 0, 1, 105, 0, 315, 0, 99, 0, 13, 0, 1, 0, 945, 0, 693, 0, 143, 0, 15, 0, 1, 945, 0, 3465, 0, 1287, 0, 195, 0, 17, 0, 1
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OFFSET
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0,8
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LINKS
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Table of n, a(n) for n=0..65.
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.
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FORMULA
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Conjecture: T(n,k) = (n+k-1)!!/(2k-1)!! for n+k even, T(n,k) = 0 otherwise. - Jean-François Alcover, Feb 11 2019
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EXAMPLE
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Triangle begins:
1,
0, 1,
1, 0, 1,
0, 3, 0, 1,
3, 0, 5, 0, 1,
0, 15, 0, 7, 0, 1,
15, 0, 35, 0, 9, 0, 1,
0, 105, 0, 63, 0, 11, 0, 1,
105, 0, 315, 0, 99, 0, 13, 0, 1,
0, 945, 0, 693, 0, 143, 0, 15, 0, 1,
945, 0, 3465, 0, 1287, 0, 195, 0, 17, 0, 1,
...
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CROSSREFS
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Sequence in context: A126595 A286096 A247622 * A179898 A099174 A066325
Adjacent sequences: A256034 A256035 A256036 * A256038 A256039 A256040
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KEYWORD
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nonn,tabl,changed
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AUTHOR
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N. J. A. Sloane, Mar 14 2015
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STATUS
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approved
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