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A256041 Triangle read by rows: number of idempotent basis elements of rank k in Brauer monoid B_n. 0
1, 0, 1, 0, 0, 1, 0, 6, 0, 1, 0, 0, 24, 0, 1, 0, 120, 0, 60, 0, 1, 0, 0, 1080, 0, 120, 0, 1, 0, 5040, 0, 5040, 0, 210, 0, 1, 0, 0, 80640, 0, 16800, 0, 336, 0, 1, 0, 362880, 0, 604800, 0, 45360, 0, 504, 0, 1, 0, 0, 9072000, 0, 3024000, 0, 105840, 0, 720, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

Also the Bell transform of A005212(n+1). For the definition of the Bell transform see A264428. - Peter Luschny, Jan 29 2016

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, 2014.

EXAMPLE

Triangle begins:

1,

0, 1,

0, 0, 1,

0, 6, 0, 1,

0, 0, 24, 0, 1,

0, 120, 0, 60, 0, 1,

0, 0, 1080, 0, 120, 0, 1,

0, 5040, 0, 5040, 0, 210, 0, 1,

0, 0, 80640, 0, 16800, 0, 336, 0, 1,

0, 362880, 0, 604800, 0, 45360, 0, 504, 0, 1,

0, 0, 9072000, 0, 3024000, 0, 105840, 0, 720, 0, 1,

...

MAPLE

# The function BellMatrix is defined in A264428.

BellMatrix(n -> `if`(n::odd, 0, (n+1)!), 9); # Peter Luschny, Jan 29 2016

MATHEMATICA

BellMatrix[f_, len_] := With[{t = Array[f, len, 0]}, Table[BellY[n, k, t], {n, 0, len - 1}, {k, 0, len - 1}]];

B = BellMatrix[Function[n, If[OddQ[n], 0, (n + 1)!]], rows = 12];

Table[B[[n, k]], {n, 1, rows}, {k, 1, n}] // Flatten (* Jean-Fran├žois Alcover, Jun 28 2018, after Peter Luschny *)

CROSSREFS

Sequence in context: A192072 A060297 A240315 * A137378 A293071 A084680

Adjacent sequences:  A256038 A256039 A256040 * A256042 A256043 A256044

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane, Mar 14 2015

STATUS

approved

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Last modified April 23 22:17 EDT 2019. Contains 322388 sequences. (Running on oeis4.)