OFFSET
0,5
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).
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, ...
1, 2, 3, 4, 5, 6, ...
1, 10, 21, 34, 49, 66, ...
1, 56, 171, 352, 605, 936, ...
1, 346, 1521, 3946, 8065, 14346, ...
1, 2252, 14283, 46744, 113525, 231876, ...
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
nonn,tabl
AUTHOR
Seiichi Manyama, Jul 10 2020
STATUS
approved