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 A344728 #20 Jan 17 2024 10:44:09 %S A344728 12,79,419,2036,9435,42449,187187,813592,3497988,14912910,63151022, %T A344728 265958200,1114981465,4656455685,19383036675,80456688240,333146169840, %U A344728 1376479675890,5676426414810,23369047049400,96060414949590 %N A344728 a(n) = (9*n/4 - 51/8 - 5/(16*n-24) + 1/n + 6/(n+1))*binomial(2*n-2,n-1). %C A344728 Conjecture: a(n) is the number of linear intervals in the tilting posets of type D_n. An interval is linear if it is isomorphic to a total order. The conjecture has been checked up to the term 187187 for n = 9. %H A344728 Michael De Vlieger, <a href="/A344728/b344728.txt">Table of n, a(n) for n = 3..1659</a> %H A344728 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 A344728 Array[(9/4 # - 51/8 - 5/8/(2 # - 3) + 1/# + 6/(# + 1))*Binomial[2 # - 2, # - 1] &, 21, 3] (* _Michael De Vlieger_, Jan 17 2024 *) %o A344728 (Sage) %o A344728 def a(n): %o A344728 return (9/4*n-51/8-5/8/(2*n-3)+1/n+6/(n+1))*binomial(2*n-2,n-1) %o A344728 (PARI) a(n) = (9*n/4-51/8-5/(16*n-24)+1/n+6/(n+1))*binomial(2*n-2,n-1) \\ _Felix Fröhlich_, May 27 2021 %Y A344728 For the tilting posets of types A and B, see A344136, A344717. %Y A344728 For the Cambrian lattices of types A, B and D, see A344136, A344228, A344321. %Y A344728 For similar sequences, see A344191, A344216. %K A344728 nonn,easy %O A344728 3,1 %A A344728 _F. Chapoton_, May 27 2021