OFFSET
0,8
LINKS
G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened
F. R. Bernhart, Catalan, Motzkin and Riordan numbers, Discr. Math., 204 (1999), 73-112.
D. Callan, A recursive bijective approach to counting permutations containing 3-letter patterns, arXiv:math/0211380 [math.CO], 2002.
FindStat - Combinatorial Statistic Finder, The number of touch points of a Dyck path., The number of initial rises of a Dyck paths., The number of nodes on the left branch of the tree., The number of subtrees.
A. Robertson, D. Saracino and D. Zeilberger, Refined restricted permutations, arXiv:math/0203033 [math.CO], 2002.
FORMULA
EXAMPLE
Triangle starts
0;
0, 1;
0, 1, 1;
0, 2, 2, 1;
0, 5, 5, 3, 1;
0, 14, 14, 9, 4, 1;
0, 42, 42, 28, 14, 5, 1;
0, 132, 132, 90, 48, 20, 6, 1;
0, 429, 429, 297, 165, 75, 27, 7, 1;
0, 1430, 1430, 1001, 572, 275, 110, 35, 8, 1;
0, 4862, 4862, 3432, 2002, 1001, 429, 154, 44, 9, 1;
...
MATHEMATICA
Table[Binomial[2*r - s - 1, r - 1] - Binomial[2*r - s - 1, r], {r, 0, 10}, {s, 0, r}] // Flatten (* G. C. Greubel, Jan 08 2017 *)
PROG
(PARI) tabl(nn) = { print(0); for (r=1, nn, for (s=0, r, print1(binomial(2*r-s-1, r-1)-binomial(2*r-s-1, r), ", "); ); print(); ); } \\ Michel Marcus, Nov 01 2013
(Magma) /* as triangle */ [[[0] cat [Binomial(2*r-s-1, r-1)- Binomial(2*r-s-1, r): s in [1..r]]: r in [0..10]]]; // Vincenzo Librandi, Jan 09 2017
CROSSREFS
The three triangles A059365, A106566 and A099039 are the same except for signs and the leading term.
Essentially the same as A033184.
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Jan 28 2001
STATUS
approved