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 A344717 #21 Jan 17 2024 10:35:35 %S A344717 6,34,169,791,3576,15807,68783,295867,1261468,5341128,22487906, %T A344717 94244294,393439840,1637091585,6792664635,28115240595,116120791380, %U A344717 478689505140,1969993524510,8095052323410,33218808108720,136148925337230,557389537873974,2279607910207326 %N A344717 a(n) = (3n - 9/2 - 1/n + 6/(n+1))*binomial(2n-2,n-1). %C A344717 Conjecture: These are the number of linear intervals in the tilting posets of type B_n. An interval is linear if it is isomorphic to a total order. The conjecture has been checked up to the term 295867 for n = 9. %H A344717 Michael De Vlieger, <a href="/A344717/b344717.txt">Table of n, a(n) for n = 2..1658</a> %H A344717 Clément Chenevière, <a href="https://theses.hal.science/tel-04255439">Enumerative study of intervals in lattices of Tamari type</a>, Ph. D. thesis, Univ. Strasbourg (France), Ruhr-Univ. Bochum (Germany), HAL tel-04255439 [math.CO], 2024. See p. 152. %t A344717 Array[(3 # - 9/2 - 1/# + 6/(# + 1))*Binomial[2 # - 2, # - 1] &, 24, 2] (* _Michael De Vlieger_, Jan 17 2024, after Sage *) %o A344717 (Sage) %o A344717 def a(n): %o A344717 return (3*n-9/2-1/n+6/(n+1))*binomial(2*n-2,n-1) %Y A344717 For the tilting posets of type A, see A344136. %Y A344717 For the Cambrian lattices of types A, B and D, see A344136, A344228, A344321. %Y A344717 For similar sequences, see A344191, A344216. %K A344717 nonn %O A344717 2,1 %A A344717 _F. Chapoton_, May 27 2021