OFFSET
0,9
COMMENTS
Column k is the diagonal of the rational function 1 / (1 + y + z + x*y + y*z - k*z*x - (k-1)*x*y*z).
Column k is the diagonal of the rational function 1 / ((1-x)*(1-y)*(1-z) + k*x*y*z).
LINKS
Seiichi Manyama, Antidiagonals n = 0..139, flattened
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, ...
1, 0, -1, -2, -3, -4, ...
1, -6, -11, -14, -15, -14, ...
1, 0, 47, 136, 261, 416, ...
1, 90, 241, 106, -639, -2294, ...
1, 0, -2281, -8492, -17523, -25624, ...
MATHEMATICA
Unprotect[Power]; 0^0 = 1; T[n_, k_] := Sum[(-k)^j * Binomial[n, j]^3, {j, 0, n}]; Table[T[k, n - k], {n, 0, 10}, {k, 0, n}] // Flatten (* Amiram Eldar, Jul 11 2020 *)
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Seiichi Manyama, Jul 10 2020
STATUS
approved