OFFSET
0,3
LINKS
Seiichi Manyama, Antidiagonals n = 0..139, flattened
FORMULA
A(n,k) = (-1)^n * Sum_{j=0..floor(n/k)} (-1)^(((k+1) mod 2) * j) * binomial(n+k-1,k*j+k-1).
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, 1, 1, ...
-2, -2, -3, -4, -5, -6, -7, -8, ...
4, 2, 6, 10, 15, 21, 28, 36, ...
-8, 0, -11, -20, -35, -56, -84, -120, ...
16, -4, 21, 34, 70, 126, 210, 330, ...
-32, 8, -42, -48, -127, -252, -462, -792, ...
64, -8, 85, 48, 220, 461, 924, 1716, ...
-128, 0, -171, 0, -385, -780, -1717, -3432, ...
256, 16, 342, -164, 715, 1209, 3017, 6434, ...
MATHEMATICA
A[n_, k_] := (-1)^n * Sum[(-1)^(Mod[k+1, 2] * j) * Binomial[n + k - 1, k*j + k - 1], {j, 0, Floor[n/k]}]; Table[A[n - k, k], {n, 0, 11}, {k, n, 1, -1}] // Flatten (* Amiram Eldar, May 25 2021 *)
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Seiichi Manyama, Mar 16 2019
STATUS
approved