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 A137211 #18 Feb 06 2020 16:10:31
%S A137211 1,1,1,1,2,3,1,5,12,22,1,14,55,140,285,1,42,273,969,2530,5481,1,132,
%T A137211 1428,7084,23751,62832,141778,1,429,7752,53820,231880,749398,1997688,
%U A137211 4638348,1,1430,43263,420732,2330445,9203634,28989675,77652024
%N A137211 Generalized or s-Catalan numbers.
%C A137211 From _R. J. Mathar_, May 04 2008: (Start)
%C A137211 This is a triangular section of Stanica's array of s-Catalan numbers, with rows A000108, A001764, A002293-A002296, A007556, A062994, A059968,... read along diagonals in A062993 and A070914:
%C A137211 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
%C A137211 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, ...
%C A137211 1, 1, 3, 12, 55, 273, 1428, 7752, 43263, 246675, 1430715, ...
%C A137211 1, 1, 4, 22, 140, 969, 7084, 53820, 420732, 3362260, 27343888, ...
%C A137211 1, 1, 5, 35, 285, 2530, 23751, 231880, 2330445, 23950355, 250543370, ...
%C A137211 1, 1, 6, 51, 506, 5481, 62832, 749398, 9203634, 115607310, 1478314266, ...
%C A137211 1, 1, 7, 70, 819, 10472, 141778, 1997688, 28989675, 430321633, 6503352856, ...
%C A137211 1, 1, 8, 92, 1240, 18278, 285384, 4638348, 77652024, 1329890705, 23190029720, ...
%C A137211 1, 1, 9, 117, 1785, 29799, 527085, 9706503, 184138713, 3573805950, 70625252863, ...
%C A137211 1, 1, 10, 145, 2470, 46060, 910252, 18730855, 397089550, 8612835715, 190223180840, ...
%C A137211 (End)
%C A137211 The Fuss-Catalan numbers are Cat(d,k)= [1/(k*(d-1)+1)]*binomial(k*d,k) and enumerate the number of (d+1)-gon partitions of a (k*(d-1)+2)-gon (cf. Whieldon and Schuetz link for this interpretation and others), so the (k+1)-th column of Stanica's array enumerates the number of (n+1)-gon partitions of a (k*(n-1)+2)-gon. Cf. A000326 (k=3), A100157 (k=4) and A234043 (k=5). - _Tom Copeland_, Oct 05 2014
%H A137211 Heinrich Niederhausen, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v9i1r33">Catalan Traffic at the Beach</a>, Electronic Journal of Combinatorics, Volume 9 (2002), #R33.
%H A137211 A. Regev, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL16/Regev/regev4.html">The Central Component of a Triangulation</a>, J. Int. Seq. 16 (2013) #13.4.1
%H A137211 Alison Schuetz and Gwyneth Whieldon, <a href="http://arxiv.org/abs/1401.7194">Polygonal Dissections and Reversions of Series</a>, arXiv:1401.7194 [math.CO], 2014.
%H A137211 P. Stanica, <a href="http://dx.doi.org/10.1016/S0022-314X(02)00125-7">p^q-Catalan numbers and squarefree binomial coefficients</a>, J. Numb. Theory 100 (2003) 203-216.
%F A137211 T(n,m) = binomial(m*n,n)/((m-1)*n+1).
%e A137211 {1},
%e A137211 {1, 1},
%e A137211 {1, 2, 3},
%e A137211 {1, 5, 12, 22},
%e A137211 {1, 14, 55, 140, 285},
%e A137211 {1, 42, 273, 969, 2530, 5481},
%e A137211 {1, 132, 1428, 7084, 23751, 62832, 141778},
%e A137211 {1, 429, 7752, 53820, 231880, 749398, 1997688, 4638348}
%t A137211 t[n_, m_] := Binomial[m*n, n]/((m - 1)*n + 1); a = Table[Table[t[n, m], {m, 1, n + 1}], {n, 0, 10}]; Flatten[a]
%K A137211 nonn
%O A137211 1,5
%A A137211 _Roger L. Bagula_, Mar 05 2008
%E A137211 Edited by _N. J. A. Sloane_, May 16 2008