OFFSET
0,5
LINKS
Seiichi Manyama, Antidiagonals n = 0..139, flattened
FORMULA
A(n,k) = Sum_{j=0..floor(n/k)} (-1)^j * binomial(n+k-1,k*j+k-1).
A(n,2*k) = Sum_{i=0..n} Sum_{j=0..n-i} (-1)^j * binomial(i+k-1,k*j+k-1) * binomial(n-i+k-1,k*j+k-1). - Seiichi Manyama, Apr 07 2019
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, 1, 1, ...
0, 2, 3, 4, 5, 6, 7, 8, ...
0, 2, 6, 10, 15, 21, 28, 36, ...
0, 0, 9, 20, 35, 56, 84, 120, ...
0, -4, 9, 34, 70, 126, 210, 330, ...
0, -8, 0, 48, 125, 252, 462, 792, ...
0, -8, -27, 48, 200, 461, 924, 1716, ...
0, 0, -81, 0, 275, 780, 1715, 3432, ...
0, 16, -162, -164, 275, 1209, 2989, 6434, ...
MATHEMATICA
A[n_, k_] := SeriesCoefficient[1/((1-x)^k + x^k), {x, 0, n}];
Table[A[n-k+1, k], {n, 0, 11}, {k, n+1, 1, -1}] // Flatten (* Jean-François Alcover, Mar 20 2019 *)
CROSSREFS
AUTHOR
Seiichi Manyama, Mar 16 2019
STATUS
approved