A380912 Two-Catalan Triangle read by rows, for n>=0 and k>=0.
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, 603, 1585, 2025, 1890, 1398, 837, 405, 155, 45, 9, 1, 4213, 11298, 15026, 14938, 12078, 8162, 4642, 2211, 869, 274, 66, 11, 1, 30537, 83097, 113841, 118482, 102102, 75075, 47619, 26091, 12285, 4914, 1638, 441, 91, 13, 1
Offset: 0
Examples
Triangle begins: 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; 603, 1585, 2025, 1890, 1398, 837, 405, 155, 45, 9, 1; ...
Links
- Yousra Ghemit and Moussa Ahmia, Two-Catalan numbers: combinatorial interpretation and log-convexity, UPB Sci. Bull., Series A (2024) Vol 86, Iss. 4. See Table 2 p. 94.
Programs
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PARI
t(n, k) = polcoef((1 + x + x^2)^n, k); \\ A027907 T(n, k) = t(2*n, 2*n+k) - t(2*n, 2*n+k+1); row(n) = vector(2*n+1, k, T(n,k-1));
Comments