OFFSET
0,5
LINKS
Fangfang Cai, Qing-Hu Hou, Yidong Sun, Arthur L.B. Yang, Combinatorial identities related to 2×2 submatrices of recursive matrices, arXiv:1808.05736 [math.CO], 2018.
Yidong Sun and Fei Ma, Minors of a Class of Riordan Arrays Related to Weighted Partial Motzkin Paths, arXiv preprint arXiv:1305.2015 [math.CO], 2013.
Yidong Sun and Fei Ma, Four transformations on the Catalan triangle, arXiv preprint arXiv:1305.2017 [math.CO], 2013.
Yidong Sun and Fei Ma, Some new binomial sums related to the Catalan triangle, Electronic Journal of Combinatorics 21(1) (2014), #P1.33
EXAMPLE
Triangle begins:
1;
0, 1;
0, 3, 1;
0, 14, 10, 1;
0, 84, 90, 21, 1;
0, 594, 825, 308, 36, 1;
...
MATHEMATICA
nn = 9;
c[n_, k_] := Binomial[2n-k, n] (k+1)/(n+1);
a[0, 0] = 1;
a[n_, k_] := Table[c[n+k+i-1, 2k+j-1], {i, 1, 2}, {j, 1, 2}] // Det;
Table[a[n, k], {n, 0, nn}, {k, 0, n}] // Flatten (* Jean-François Alcover, Aug 12 2018 *)
PROG
(PARI) C(n, k) = (k<=n)*binomial(2*n-k, n)*(k+1)/(n+1);
aX(nn) = {for (n = 0, nn, for (k = 0, n, print1(matdet(matrix(2, 2, i, j, C(n+k+i-1, 2*k+j-1))), ", "); ); print(); ); } \\ Michel Marcus, Feb 13 2014
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Aug 26 2013
EXTENSIONS
More terms from Michel Marcus, Feb 13 2014
A-number for Catalan triangle changed by Michel Marcus, Feb 13 2014
STATUS
approved