|
|
A307090
|
|
Number triangle T(n,k) = Sum_{j=0..n-k} (-1)^j * binomial(k,2*j) * binomial(n-k,2*j).
|
|
3
|
|
|
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, -2, -2, 1, 1, 1, 1, -5, -8, -5, 1, 1, 1, 1, -9, -17, -17, -9, 1, 1, 1, 1, -14, -29, -34, -29, -14, 1, 1, 1, 1, -20, -44, -54, -54, -44, -20, 1, 1, 1, 1, -27, -62, -74, -74, -74, -62, -27, 1, 1, 1, 1, -35, -83, -90, -74, -74, -90, -83, -35, 1, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,18
|
|
LINKS
|
|
|
EXAMPLE
|
Triangle begins:
n\k | 0 1 2 3 4 5 6 7 8
----+-------------------------------------
0 | 1;
1 | 1, 1;
2 | 1, 1, 1;
3 | 1, 1, 1, 1;
4 | 1, 1, 0, 1, 1;
5 | 1, 1, -2, -2, 1, 1;
6 | 1, 1, -5, -8, -5, 1, 1;
7 | 1, 1, -9, -17, -17, -9, 1, 1;
8 | 1, 1, -14, -29, -34, -29, -14, 1, 1;
|
|
MATHEMATICA
|
T[n_, k_] := Sum[(-1)^j * Binomial[k, 2*j] * Binomial[n - k, 2*j], {j, 0, n - k}]; Table[T[n, k], {n, 0, 11}, {k, 0, n}] // Flatten (* Amiram Eldar, May 20 2021 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|