|
| |
|
|
A059365
|
|
Another version of the Catalan triangle: T(r,s) = binomial(2*r-s-1,r-1)-binomial(2*r-s-1,r), r>=0, 0<=s<=r.
|
|
29
|
|
|
|
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
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,8
|
|
|
REFERENCES
|
F. R. Bernhart, Catalan, Motzkin and Riordan numbers, Discr. Math., 204 (1999) 73-112.
|
|
|
LINKS
|
Table of n, a(n) for n=0..63.
D. Callan, A recursive bijective approach to counting permutations...
A. Robertson, D. Saracino and D. Zeilberger, Refined restricted permutations.
|
|
|
FORMULA
|
Essentially the same triangle as [0, 1, 1, 1, 1, 1, 1, ...] DELTA A000007, where DELTA is Deleham's operator defined in A084938, but the first term is T(0, 0)= 0.
|
|
|
EXAMPLE
|
0; 0,1; 0,1,1; 0,2,2,1; 0,5,5,3,1; ...
|
|
|
CROSSREFS
|
See also the triangle in A009766. First 2 diagonals both give A000108, next give A000245, A002057.
Cf. A009766 A000007 A084938 A000108.
The three triangles A059365, A106566 and A099039 are the same except for signs and the leading term.
Essentially the same as A033184.
The following are all versions of (essentially) the same Catalan triangle: A009766, A030237, A033184, A059365, A099039, A106566, A130020, A047072.
Diagonals give A000108 A000245 A002057 A000344 A003517 A000588 A003518 A003519 A001392, ...
Sequence in context: A128497 A011434 A147746 * A106566 A099039 A205574
Adjacent sequences: A059362 A059363 A059364 * A059366 A059367 A059368
|
|
|
KEYWORD
|
nonn,tabl
|
|
|
AUTHOR
|
N. J. A. Sloane, Jan 28 2001
|
|
|
STATUS
|
approved
|
| |
|
|
