A370758 Number of ramified partitions (I,J) of size n, where J is balanced with respect to up brackets and down brackets.

1, 1, 5, 48, 747, 17040, 531810, 21634515, 1107593235, 69482175840, 5229801016650, 464302838867175, 47939015445032250, 5688437019459319125, 767922887039461928775, 116915022542869964287875, 19922514312608630279431875, 3774243527942494591068084000, 790220453914362566924533955250

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

Cf. A343254.

Sequence in context: A360235 A108207 A127091 * A352254 A346183 A224510

Adjacent sequences: A370755 A370756 A370757 * A370759 A370760 A370761

Keyword

nonn

Author

Diego Arcis, Feb 29 2024

Status

approved