|
Search: id:A091044
|
|
|
| A091044 |
|
One half of odd numbered entries of even numbered rows of Pascal's triangle A007318. |
|
+0
2
|
|
| 1, 2, 2, 3, 10, 3, 4, 28, 28, 4, 5, 60, 126, 60, 5, 6, 110, 396, 396, 110, 6, 7, 182, 1001, 1716, 1001, 182, 7, 8, 280, 2184, 5720, 5720, 2184, 280, 8, 9, 408, 4284, 15912, 24310, 15912, 4284, 408, 9, 10, 570, 7752, 38760, 83980, 83980, 38760, 7752, 570, 10, 11
(list; table; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
The odd numbered columns of this triangle can be reduced: see triangle A091043.
The odd numbered rows coincide with the ones of the reduced triangle A091043.
binomial(2*n,2*m+1) is even for n>=m+1>=1, hence every a(n,m) is a positive integer.
The GCD (greatest common divisor) of the entries of each odd numbered row n=2*k+1, k>=0, is 1.
The GCD of the entries of the even numbered row n=2*k, k>=1, is A006519(n) (highest power of 2 in n=2*k).
|
|
LINKS
|
W. Lang, First 9 rows.
|
|
FORMULA
|
a(n, m)= binomial(2*n, 2*m+1)/2, n>=m+1>=1, else 0.
|
|
EXAMPLE
|
[1];[2,2];[3,10,3];[4,28,28,4];[5,60,126,60,5];[6,110,396,396,110,6];...
n=6=2*3: GCD(6,110,396)=2=A006519(6); n=5:
GCD(5,60,126)=1=A006519(5).
|
|
CROSSREFS
|
Sequence in context: A019234 A032172 A032103 this_sequence A079661 A067579 A019143
Adjacent sequences: A091041 A091042 A091043 this_sequence A091045 A091046 A091047
|
|
KEYWORD
|
nonn,easy,tabl
|
|
AUTHOR
|
Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Jan 23 2004
|
|
|
Search completed in 0.002 seconds
|
