A256041 Triangle read by rows: number of idempotent basis elements of rank k in Brauer monoid B_n.

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

Offset: 0

Author

N. J. A. Sloane, Mar 14 2015

Keywords

• nonn
• tabl

Comments

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

Examples

			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,
...
		

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.

Crossrefs

Cf. A005212, A264428.

Programs

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 *)