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 A090182 #33 May 05 2019 07:51:21
%S A090182 1,1,1,1,1,1,1,2,1,1,1,5,3,1,1,1,14,17,4,1,1,1,42,171,43,5,1,1,1,132,
%T A090182 3113,1252,89,6,1,1,1,429,106419,104098,5885,161,7,1,1,1,1430,7035649,
%U A090182 25511272,1518897,20466,265,8,1,1,1,4862,915028347,18649337311,1558435125,12833546,57799,407,9,1,1
%N A090182 Triangle T(n,k), 0 <= k <= n, composed of k-Catalan numbers.
%H A090182 Alois P. Heinz, <a href="/A090182/b090182.txt">Rows n = 0..55, flattened</a>
%H A090182 Lun Lv, Zhihong Liu, <a href="https://dx.doi.org/10.1109%2FISCID.2016.1084">Some Identities Related to Restricted Lattice Paths</a>, 2016 9th International Symposium on Computational Intelligence and Design (ISCID), pp. 338-340.
%e A090182 Triangle begins:
%e A090182 1;
%e A090182 1, 1;
%e A090182 1, 1, 1;
%e A090182 1, 2, 1, 1;
%e A090182 1, 5, 3, 1, 1;
%e A090182 1, 14, 17, 4, 1, 1;
%e A090182 1, 42, 171, 43, 5, 1, 1;
%e A090182 1, 132, 3113, 1252, 89, 6, 1, 1;
%e A090182 1, 429, 106419, 104098, 5885, 161, 7, 1, 1;
%e A090182 1, 1430, 7035649, 25511272, 1518897, 20466, 265, 8, 1, 1;
%e A090182 This sequence formatted as a square array:
%e A090182 1, 1, 1, 1, 1, 1, 1, 1, ...
%e A090182 1, 1, 2, 5, 14, 42, 132, 429, ...
%e A090182 1, 1, 3, 17, 171, 3113, 106419, 7035649, ...
%e A090182 1, 1, 4, 43, 1252, 104098, 25511272, 18649337311, ...
%e A090182 1, 1, 5, 89, 5885, 1518897, 1558435125, 6386478643785, ...
%e A090182 1, 1, 6, 161, 20466, 12833546, 40130703276, 627122621447281, ...
%p A090182 T:= proc(n, k) option remember; `if`(k=n, 1, add(
%p A090182 T(j+k, k)*T(n-j-1, k)*k^j, j=0..n-k-1))
%p A090182 end:
%p A090182 seq(seq(T(n, k), k=0..n), n=0..12); # _Alois P. Heinz_, Aug 10 2017
%t A090182 nmax = 10; col[k_] := col[k] = Module[{A}, A[_] = 0; Do[A[x_] = Normal[1/(1 - x*A[k*x]) + O[x]^(nmax-k+1)], {nmax-k+1}]; CoefficientList[A[x], x]];
%t A090182 T[n_, k_] := col[k][[n-k+1]];
%t A090182 Table[T[n, k], {n, 0, nmax}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, May 05 2019, using g.f. given for column sequences *)
%Y A090182 The column sequences (without leading zeros) are A000012, A000108 (Catalan), A015083, A015084, A015085, A015086, A015089, A015091, A015092, A015093, A015095, A015096 for k=0..11.
%Y A090182 T(2n,n) gives A290777.
%Y A090182 Cf. A290759.
%K A090182 easy,nonn,tabl
%O A090182 0,8
%A A090182 _Philippe Deléham_, Jan 20 2004, Oct 16 2008