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 A380912 #7 Feb 08 2025 11:11:47 %S A380912 1,1,1,1,3,6,6,3,1,15,36,40,29,15,5,1,91,232,280,238,154,76,28,7,1, %T A380912 603,1585,2025,1890,1398,837,405,155,45,9,1,4213,11298,15026,14938, %U A380912 12078,8162,4642,2211,869,274,66,11,1,30537,83097,113841,118482,102102,75075,47619,26091,12285,4914,1638,441,91,13,1 %N A380912 Two-Catalan Triangle read by rows, for n>=0 and k>=0. %C A380912 It appears that this triangle is made of the even rows of A089942. %H A380912 Yousra Ghemit and Moussa Ahmia, <a href="https://www.scientificbulletin.upb.ro/rev_docs_arhiva/rezef9_607301.pdf">Two-Catalan numbers: combinatorial interpretation and log-convexity</a>, UPB Sci. Bull., Series A (2024) Vol 86, Iss. 4. See Table 2 p. 94. %F A380912 T(n,k) = A027907(2*n,k) - A027907(2*n,k+1). %e A380912 Triangle begins: %e A380912 1; %e A380912 1, 1, 1; %e A380912 3, 6, 6, 3, 1; %e A380912 15, 36, 40, 29, 15, 5, 1; %e A380912 91, 232, 280, 238, 154, 76, 28, 7, 1; %e A380912 603, 1585, 2025, 1890, 1398, 837, 405, 155, 45, 9, 1; %e A380912 ... %o A380912 (PARI) t(n, k) = polcoef((1 + x + x^2)^n, k); \\ A027907 %o A380912 T(n, k) = t(2*n, 2*n+k) - t(2*n, 2*n+k+1); %o A380912 row(n) = vector(2*n+1, k, T(n,k-1)); %Y A380912 Cf. A027907, A089942, A380899. %K A380912 nonn,tabf %O A380912 0,5 %A A380912 _Michel Marcus_, Feb 08 2025