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 A339460 #24 Dec 26 2020 16:06:00
%S A339460 1,2,8,42,262,1820,4,13756,32,110394,280,928790,2328,4,8110104,21294,
%T A339460 56,73040142,191396,540,24,674775338,1798624,5214,472,6370633938,
%U A339460 17113152,48240,6482,32,61269105780,168043112,450616,83804,464,32,0,4
%N A339460 Triangle read by rows: T(n,k) is the number of k-element equivalence classes of closed meanders with 2n points.
%C A339460 Two closed meanders s and t with 2n points are equivalent iff their corresponding permutations s(1) s(2) ... s(2n) and t(1) t(2) ... t(2n) have the same absolute difference sequence, i.e. |s(i+1) - s(i)| = |t(i+1) - t(i)| for all i = 1,2,..,2n, where s(1) = t(1) = s(2n+1) = t(2n+1) = 1.
%H A339460 M. De Biasi, <a href="https://doi.org/10.37236/4086">Permutation Reconstruction from Differences</a>, Electronic Journal of Combinatorics, Volume 21 No. 4 (2014), P4.3 (23 pages).
%H A339460 A. Panayotopoulos, <a href="https://doi.org/10.1007/s11786-018-0389-6">On Meandric Colliers</a>, Mathematics in Computer Science, (2018).
%H A339460 J. Sawada and R. Li, <a href="https://doi.org/10.37236/2404">Stamp foldings, semi-meanders, and open meanders: fast generation algorithms</a>, Electronic Journal of Combinatorics, Volume 19 No. 2 (2012), P#43 (16 pages).
%F A339460 Sum_{k >= 1} k*T(n,k) = A005315(n) (closed meandric numbers).
%e A339460 Triangle begins:
%e A339460 1;
%e A339460 2;
%e A339460 8;
%e A339460 42;
%e A339460 262;
%e A339460 1820, 4;
%e A339460 13756, 32;
%e A339460 110394, 280;
%e A339460 928790, 2328, 4;
%e A339460 8110104, 21294, 56;
%e A339460 73040142, 191396, 540, 24;
%e A339460 674775338, 1798624, 5214, 472;
%e A339460 6370633938, 17113152, 48240, 6482, 32;
%e A339460 61269105780, 168043112, 450616, 83804, 464, 32, 0, 4;
%e A339460 ...
%e A339460 For n = 6 there exist four 2-element equivalence classes:
%e A339460 1st class consists of permutations (1, 2, 5, 6, 7, 4, 3, 8, 9, 12, 11, 10) and (1, 2, 5, 4, 3, 6, 7, 12, 11, 8, 9, 10) having difference sequence: (1, 3, 1, 1, 3, 1, 5, 1, 3, 1, 1, 9).
%e A339460 2nd class consists of permutations (1, 12, 9, 10, 11, 8, 7, 2, 3, 6, 5, 4) and (1, 12, 9, 8, 7, 10, 11, 6, 5, 2, 3, 4) having difference sequence: (11, 3, 1, 1, 3, 1, 5, 1, 3, 1, 1, 3).
%e A339460 3rd class consists of permutations (1, 10, 9, 8, 11, 12, 7, 6, 3, 4, 5, 2) and (1, 10, 11, 12, 9, 8, 3, 4, 7, 6, 5, 2) having difference sequence: (9, 1, 1, 3, 1, 5, 1, 3, 1, 1, 3, 1).
%e A339460 4th class consists of permutations (1, 4, 5, 6, 3, 2, 7, 8, 11, 10, 9, 12) and (1, 4, 3, 2, 5, 6, 11, 10, 7, 8, 9, 12) having difference sequence: (3, 1, 1, 3, 1, 5, 1, 3, 1, 1, 3, 11).
%Y A339460 Cf. A005315.
%K A339460 tabf,nonn
%O A339460 1,2
%A A339460 _Gerasimos Pergaris_, Dec 06 2020