|
| |
|
|
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
|
|
|
CROSSREFS
|
Sequence in context: A192072 A060297 A240315 * A137378 A084680 A051626
Adjacent sequences: A256038 A256039 A256040 * A256042 A256043 A256044
|
|
|
KEYWORD
|
nonn,tabl
|
|
|
AUTHOR
|
N. J. A. Sloane, Mar 14 2015
|
|
|
STATUS
|
approved
|
| |
|
|
