|
Search: id:A107711
|
|
|
| A107711 |
|
Triangle read by rows: T(0,0)=1, T(n,m) = binomial(n,m) GCD(n,m)/n. |
|
+0
2
|
|
| 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 5, 10, 5, 1, 1, 1, 1, 3, 5, 5, 3, 1, 1, 1, 1, 7, 7, 35, 7, 7, 1, 1, 1, 1, 4, 28, 14, 14, 28, 4, 1, 1, 1, 1, 9, 12, 42, 126, 42, 12, 9, 1, 1, 1, 1, 5, 15, 30, 42, 42, 30, 15, 5, 1, 1, 1, 1, 11, 55, 165, 66, 462, 66, 165, 55, 11, 1, 1
(list; table; graph; listen)
|
|
|
OFFSET
|
0,13
|
|
|
COMMENT
|
T(0,0) is an indeterminate, but 1 seems a logical value to assign it. T(n,0) = T(n,1) = T(n,n-1) = T(n,n) = 1.
T(2n,n)=A001700(n-1) (n>=1) - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 13 2005
|
|
LINKS
|
Leroy Quet, Home Page (listed in lieu of email address)
|
|
EXAMPLE
|
T(6,2)=5 because binomial(6,2)*gcd(6,2)/6=15*2/6=5/
Triangle begins:
1;
1,1;
1,1,1;
1,1,1,1;
1,1,3,1,1;
1,1,2,2,1,1;
|
|
MAPLE
|
a:=proc(n, k) if n=0 and k=0 then 1 elif k<=n then binomial(n, k)*gcd(n, k)/n else 0 fi end: for n from 0 to 13 do seq(a(n, k), k=0..n) od; # yields sequence in triangular form (Deutsch)
|
|
CROSSREFS
|
Cf. A007318.
Cf. A001700.
Sequence in context: A109673 A023591 A165661 this_sequence A061893 A078530 A010276
Adjacent sequences: A107708 A107709 A107710 this_sequence A107712 A107713 A107714
|
|
KEYWORD
|
tabl,nonn
|
|
AUTHOR
|
Leroy Quet Jun 10 2005
|
|
EXTENSIONS
|
More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 13 2005
|
|
|
Search completed in 0.002 seconds
|
