|
Search: id:A050169
|
|
|
| A050169 |
|
Triangle read by rows: T(n,k)=GCD(C(n,k),C(n,k-1)), n >= 1, 1<=k<=n. |
|
+0
3
|
|
| 1, 1, 1, 1, 3, 1, 1, 2, 2, 1, 1, 5, 10, 5, 1, 1, 3, 5, 5, 3, 1, 1, 7, 7, 35, 7, 7, 1, 1, 4, 28, 14, 14, 28, 4, 1, 1, 9, 12, 42, 126, 42, 12, 9, 1, 1, 5, 15, 30, 42, 42, 30, 15, 5, 1, 1, 11, 55, 165, 66, 462, 66, 165, 55, 11, 1, 1, 6, 22, 55, 99, 132, 132, 99, 55, 22, 6, 1, 1, 13, 26
(list; table; graph; listen)
|
|
|
OFFSET
|
0,5
|
|
|
COMMENT
|
Equivalently, table T(n,k)=gcd(n,k)*(n+k-1)!/(n!*k!) read by antidiagonals. - Michael Somos, Jul 19 2002
|
|
REFERENCES
|
H. Gupta, On a problem in parity, Indian J. Math., 11 (1969), 157-163. MR0260659
|
|
FORMULA
|
a(2n, n)=nth Catalan number; see A000108.
Also T(n, k)=GCD(C(n, k), C(n+1, k)).
|
|
EXAMPLE
|
1; 1,1; 1,3,1; 1,2,2,1; 1,5,10,5,1; 1,3,5,5,3,1; ...
|
|
PROGRAM
|
(PARI) T(n, k)=if(n<1|k<1, 0, gcd(n, k)*(n+k-1)!/n!/k!)
(PARI) T(n, k)=if(k<1|k>n, 0, gcd(n+1, k)*binomial(n, k-1)/k) - Michael Somos Mar 03 2004
|
|
CROSSREFS
|
Cf. A002784.
Sequence in context: A089338 A126209 A073166 this_sequence A064048 A016464 A030727
Adjacent sequences: A050166 A050167 A050168 this_sequence A050170 A050171 A050172
|
|
KEYWORD
|
nonn,tabl
|
|
AUTHOR
|
Clark Kimberling (ck6(AT)evansville.edu)
|
|
|
Search completed in 0.002 seconds
|
