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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 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, 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-François Alcover, Jun 28 2018, after Peter Luschny *) CROSSREFS Cf. A005212, A264428. Sequence in context: A060297 A240315 A339431 * A137378 A333275 A293071 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 January 15 13:34 EST 2021. Contains 340187 sequences. (Running on oeis4.)