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 A282698 #34 Jan 22 2018 10:19:20 %S A282698 1,1,1,1,1,4,2,2,1,10,22,22,18,13,12,1,20,112,232,382,348,456,390,420, %T A282698 334,286,1,35,392,1744,4474,8435,12732,17337,21158,27853,33940,41230, %U A282698 45048,50752,41826,33592,1,56,1092,9220,40414,123704,276324,550932,917884 %N A282698 Irregular triangle read by rows: row n gives numbers of maximal chains of lengths n-1, n, n+1, ... in the Tamari lattice T_n. %C A282698 Nelson (2017) gives first nine columns of the transposed triangle. %H A282698 Alois P. Heinz, <a href="/A282698/b282698.txt">Rows n = 1..14, flattened</a> %H A282698 Luke Nelson, <a href="https://doi.org/10.1016/j.disc.2016.11.030">A recursion on maximal chains in the Tamari lattices</a>, Discrete Mathematics 340.4 (2017): 661-677. %H A282698 Luke Nelson, <a href="https://arxiv.org/abs/1709.02987">A recursion on maximal chains in the Tamari lattices</a>, arXiv:1709.02987 [math.CO], (2017) %e A282698 Triangle begins: %e A282698 1; %e A282698 1; %e A282698 1, 1; %e A282698 1, 4, 2, 2; %e A282698 1, 10, 22, 22, 18, 13, 12; %e A282698 1, 20, 112, 232, 382, 348, 456, 390, 420, 334, 286; %e A282698 ... %e A282698 The transposed triangle, as given by Nelson, begins: %e A282698 1, 1, 1, 1, 1, 1, 1, 1, 1, ... %e A282698 1, 4, 10, 20, 35, 56, 84, ... %e A282698 2, 22, 112, 392, 1092, 2604, ... %e A282698 2, 22, 232, 1744, 9220, 37444, ... %e A282698 18, 382, 4474, 40414, 280214, ... %e A282698 13, 348, 8435, 123704, 1321879, ... %e A282698 12, 456, 12732, 276324, 4578596, ... %e A282698 390, 17337, 550932, 12512827, ... %e A282698 420, 21158, 917884, 29499764, ... %e A282698 334, 27853, 1510834, 62132126, ... %e A282698 286, 33940, 2166460, 120837274, ... %e A282698 41230, 3370312, 221484557, ... %e A282698 45048, 4810150, 393364848, ... %e A282698 50752, 7264302, 666955139, ... %e A282698 41826, 10435954, 1134705692, ... %e A282698 33592, 15227802, 1933708535, ... %e A282698 ... %p A282698 s:= proc(n) s(n):=`if`(n=0, [], [s(n-1), []]) end: %p A282698 f:= l-> l=[] or l[1]=[] and f(l[2]): %p A282698 v:= proc(l) v(l):=`if`(f(l), [], [`if`(l[1]<>[], %p A282698 [l[1][1], [l[1][2], l[2]]], [][]), %p A282698 seq([w, l[2]], w=v(l[1])), seq([l[1], w], w=v(l[2]))]) %p A282698 end: %p A282698 p:= proc(l) p(l):=`if`(f(l), 1, add(expand(x*p(w)), w=v(l))) end: %p A282698 T:= n-> (h-> seq(coeff(h, x, i), i=ldegree(h)..degree(h)))(p(s(n))): %p A282698 seq(T(n), n=1..8); # _Alois P. Heinz_, Jan 02 2018 %Y A282698 Row sums give A027686. %Y A282698 Right border gives A003121(n-1). %K A282698 nonn,tabf %O A282698 1,6 %A A282698 _N. J. A. Sloane_, Feb 25 2017 %E A282698 More terms from _Alois P. Heinz_, Jan 02 2018