OFFSET
0,2
LINKS
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;
2;
4, 1;
10, 4;
20, 21, 1;
56, 70, 6;
140, 238, 50, 1;
420, 792, 210, 8;
1176, 2604, 990, 91, 1;
...
MATHEMATICA
nn = 12;
c[n_, k_] := If[k <= n, Binomial[2n-k, n] (k+1)/(n+1), 0];
a[n_, k_] := Table[c[If[OddQ[n], (n-1)/2+k+2i-2, n/2+k+i-1], 2k+j-1], {i, 1, 2}, {j, 1, 2}] // Permanent;
Table[a[n, k], {n, 0, nn}, {k, 0, n/2}] // Flatten (* Jean-François Alcover, Aug 12 2018 *)
PROG
(PARI) C(n, k) = (k<=n)*binomial(2*n-k, n)*(k+1)/(n+1);
matperm(M)=my(n=#M, t); sum(i=1, n!, t=numtoperm(n, i); prod(j=1, n, M[j, t[j]])); \\ from Rosetta code
W(n, k) = my(nn); if (n % 2, nn = (n-1)/2; matperm(matrix(2, 2, i, j, C(nn+k+2*i-2, 2*k+j-1))), nn = n/2; matperm(matrix(2, 2, i, j, C(nn+k+i-1, 2*k+j-1))));
aW(nn) = {for (n=0, nn, for (k=0, n\2, print1(W(n, k), ", "); ); print(); ); } \\ Michel Marcus, Feb 13 2014
CROSSREFS
KEYWORD
nonn,tabf
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