OFFSET
0,5
LINKS
Seiichi Manyama, Antidiagonals n = 0..139, flattened
FORMULA
T(n,k) = Sum_{j=0..n} (k-1)^j * binomial(n+1,j) * binomial(n+1,j+1).
n * (n+2) * T(n,k) = (n+1) * (k * (2*n+1) * T(n-1,k) - (k-2)^2 * n * T(n-2,k)) for n>1.
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, ...
0, 2, 4, 6, 8, 10, ...
-3, 3, 15, 33, 57, 87, ...
0, 4, 56, 180, 400, 740, ...
10, 5, 210, 985, 2810, 6285, ...
0, 6, 792, 5418, 19824, 53550, ...
MATHEMATICA
T[n_, k_] := Sum[If[k==1 && j==0, 1, (k-1)^j] * Binomial[n + 1, j] * Binomial[n + 1, j + 1], {j, 0, n}]; Table[T[k, n - k], {n, 0, 9}, {k, 0, n}] // Flatten (* Amiram Eldar, May 05 2021 *)
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Seiichi Manyama, Jan 26 2020
STATUS
approved