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 A380899 #12 Feb 10 2025 03:13:12 %S A380899 1,1,1,1,1,4,9,11,10,6,3,1,34,90,120,120,96,64,35,15,5,1,364,1000, %T A380899 1400,1505,1351,1044,700,406,202,84,28,7,1,4269,11925,17225,19425, %U A380899 18657,15753,11845,7965,4785,2553,1197,485,165,45,9,1 %N A380899 Three-Catalan Triangle read by rows, for n>=0 and k>=0. %H A380899 Boualam Rezig and Moussa Ahmia, <a href="https://arxiv.org/abs/2502.03615">Combinatorics of three-Catalan numbers and some positivities</a>, arXiv:2502.03615 [math.CO], 2025. See Table 2 p. 5. T(4,7)=405 is a typo. %F A380899 T(n, k) = A008287(2*n, 3*n+k) - A008287(2*n, 3*n+k+1). %e A380899 Triangle begins: %e A380899 1 %e A380899 1 1 1 1 %e A380899 4 9 11 10 6 3 1 %e A380899 34 90 120 120 96 64 35 15 5 1 %e A380899 364 1000 1400 1505 1351 1044 700 406 202 84 28 7 1 %e A380899 ... %o A380899 (PARI) %o A380899 t(n, k) = polcoef((1 + x + x^2 + x^3)^n, k); \\ A008287 %o A380899 T(n, k) = t(2*n, 3*n+k) - t(2*n, 3*n+k+1); %o A380899 row(n) = vector(3*n+1, k, T(n,k-1)); %Y A380899 Row sums are A005721. %Y A380899 Cf. A008287. %K A380899 nonn,tabf %O A380899 0,6 %A A380899 _Michel Marcus_, Feb 07 2025