OFFSET
1,2
EXAMPLE
The first 3 rows are 1; 2, 1; 5, 6, 1; since the first 3 rows of the Narayana triangle in matrix format are M = [1 0 0 / 1 1 0 / 1 3 1]. Then M^2 = [1 0 0 / 2 1 0 / 5 6 1].
Triangle starts:
1;
2, 1;
5, 6, 1;
14, 30, 12, 1;
42, 140, 100, 20, 1;
...
MATHEMATICA
t[n_, k_] = Sum[1/(i*k)*(Binomial[i-1, k-1]*Binomial[i, k-1]* Binomial[n-1, i-1]*Binomial[n, i-1]), {i, k, n}];
Flatten[Table[t[n, k], {n, 1, 10}, {k, 1, n}]][[1;; 50]] (* Jean-François Alcover, Jul 21 2011 *)
CROSSREFS
KEYWORD
AUTHOR
Gary W. Adamson, Jun 07 2004
EXTENSIONS
Edited and extended by David Wasserman, Sep 24 2004
STATUS
approved