OFFSET
0,6
COMMENTS
Triangle given by A000004 DELTA A000012 where DELTA is the operator defined in A084938. - Philippe Deléham, Jul 12 2007
T(n,k) is the number of Dyck paths of semilength n having exactly k U=(1,1) steps. - Alois P. Heinz, Jun 09 2014
LINKS
Alois P. Heinz, Rows n = 0..140, flattened
FORMULA
A000108(n) preceded by n zeros, as an infinite lower triangular matrix.
EXAMPLE
First few rows of the triangle are:
1;
0, 1;
0, 0, 2;
0, 0, 0, 5;
0, 0, 0, 0, 14;
0, 0, 0, 0, 0, 42;
...
MAPLE
T:= (n, k)-> `if`(k<n, 0, binomial(2*n, n)/(n+1)):
seq(seq(T(n, k), k=0..n), n=0..15); # Alois P. Heinz, Jun 09 2014
MATHEMATICA
T[n_, n_] := CatalanNumber[n]; T[_, _] = 0;
Table[T[n, k], {n, 0, 15}, {k, 0, n}] // Flatten (* Jean-François Alcover, May 20 2016 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Jul 10 2007
EXTENSIONS
More terms from Philippe Deléham, Oct 16 2008
STATUS
approved