|
|
A143418
|
|
Triangle read by rows. T(n,k) = binomial(n,k)*(binomial(n,k)-1)/2.
|
|
3
|
|
|
1, 3, 3, 6, 15, 6, 10, 45, 45, 10, 15, 105, 190, 105, 15, 21, 210, 595, 595, 210, 21, 28, 378, 1540, 2415, 1540, 378, 28, 36, 630, 3486, 7875, 7875, 3486, 630, 36, 45, 990, 7140, 21945, 31626, 21945, 7140, 990, 45, 55, 1485, 13530, 54285, 106491, 106491
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
Row sums = A108958: (1, 6, 27, 110, 430, 1652, ...).
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
Row 4 of Pascal's triangle (1, 4, 6, 4, 1) with each term squared = (1, 16, 36, 16, 1), then subtracting (1, 4, 6, 4, 1) = (0, 12, 30, 12, 0). Dividing by 2 and deleting the zeros, we get row 4 of A143148: (6, 15, 6).
First few rows of the triangle =
1;
3, 3;
6, 15, 6;
10, 45, 45, 10;
15, 105, 190, 105, 15;
21, 210, 595, 595, 210, 21;
28, 378, 1540, 2415, 1540, 378, 28;
...
|
|
MAPLE
|
binomial(n, k)*(binomial(n, k)-1)/2 ;
end proc:
|
|
MATHEMATICA
|
Table[Binomial[n, k] (Binomial[n, k]-1)/2, {n, 20}, {k, n-1}]//Flatten (* Harvey P. Dale, Jun 14 2021 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|