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A256037 Triangle read by rows: number of R-class idempotents of rank k in Brauer monoid B_n. 0
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

LINKS

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.

FORMULA

Conjecture: T(n,k) = (n+k-1)!!/(2k-1)!! for n+k even, T(n,k) = 0 otherwise. - Jean-François Alcover, Feb 11 2019

EXAMPLE

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,

...

CROSSREFS

Sequence in context: A126595 A286096 A247622 * A179898 A099174 A066325

Adjacent sequences:  A256034 A256035 A256036 * A256038 A256039 A256040

KEYWORD

nonn,tabl,changed

AUTHOR

N. J. A. Sloane, Mar 14 2015

STATUS

approved

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Last modified February 16 18:53 EST 2019. Contains 320165 sequences. (Running on oeis4.)