OFFSET
0,3
COMMENTS
a(n) is the cardinality of the balanced ramified Brauer monoid bBr_n.
LINKS
Diego Arcis, Table of n, a(n) for n = 0..200
Francesca Aicardi, Diego Arcis, and Jesús Juyumaya, Brauer and Jones tied monoids, arXiv:2107.04170 [math.RT], 2021.
Francesca Aicardi, Diego Arcis, and Jesús Juyumaya, Brauer and Jones tied monoids, J. Pure. Appl. Algebra 227 (2023), 107161.
FORMULA
a(n) = Sum_{k=0..n/2} n!^2/(2^(2*k)*k!^2*(n-2*k)!) * A343254(n,k).
EXAMPLE
a(3) = 48 is the number of ramified partitions (I,J) of size 3, in which each block of J contains the same number of up brackets and down brackets from I, i.e., each block of J contains either no brackets from I or one up and one down bracket from I.
CROSSREFS
KEYWORD
nonn
AUTHOR
Diego Arcis, Feb 29 2024
STATUS
approved