This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A370758 #35 Apr 05 2024 00:50:29
%S A370758 1,1,5,48,747,17040,531810,21634515,1107593235,69482175840,
%T A370758 5229801016650,464302838867175,47939015445032250,5688437019459319125,
%U A370758 767922887039461928775,116915022542869964287875,19922514312608630279431875,3774243527942494591068084000,790220453914362566924533955250
%N A370758 Number of ramified partitions (I,J) of size n, where J is balanced with respect to up brackets and down brackets.
%C A370758 a(n) is the cardinality of the balanced ramified Brauer monoid bBr_n.
%H A370758 Diego Arcis, <a href="/A370758/b370758.txt">Table of n, a(n) for n = 0..200</a>
%H A370758 Francesca Aicardi, Diego Arcis, and Jesús Juyumaya, <a href="https://arxiv.org/abs/2107.04170">Brauer and Jones tied monoids</a>, arXiv:2107.04170 [math.RT], 2021.
%H A370758 Francesca Aicardi, Diego Arcis, and Jesús Juyumaya, <a href="https://doi.org/10.1016/j.jpaa.2022.107161">Brauer and Jones tied monoids</a>, J. Pure. Appl. Algebra 227 (2023), 107161.
%F A370758 a(n) = Sum_{k=0..n/2} n!^2/(2^(2*k)*k!^2*(n-2*k)!) * A343254(n,k).
%e A370758 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.
%Y A370758 Cf. A343254.
%K A370758 nonn
%O A370758 0,3
%A A370758 _Diego Arcis_, Feb 29 2024