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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
OFFSET
0,18
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
Row sums give A099587(n+1).
T(2*n,n) gives A307091.
Sequence in context: A096601 A078077 A078082 * A347630 A079674 A113193
KEYWORD
sign,tabl,look
AUTHOR
Seiichi Manyama, Mar 24 2019
STATUS
approved

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Last modified September 20 06:55 EDT 2024. Contains 376067 sequences. (Running on oeis4.)