OFFSET
0,6
LINKS
Seiichi Manyama, Antidiagonals n = 0..139, flattened
FORMULA
G.f. A_k(x) of column k satisfies A_k(x) = 1 + x * A_k(x)^k / (1 + 2 * x * A_k(x)).
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, 1, ...
1, 1, 1, 1, 1, 1, 1, ...
-2, -1, 0, 1, 2, 3, 4, ...
2, -1, -1, 2, 8, 17, 29, ...
4, 5, 0, 5, 36, 109, 240, ...
-24, -3, 2, 13, 177, 766, 2177, ...
48, -21, 0, 36, 922, 5699, 20910, ...
MATHEMATICA
T[0, k_] := 1; T[n_, k_] := Sum[(-2)^(n - j) * Binomial[n, j] * Binomial[n + (k - 1)*j, j - 1], {j, 1, n}] / n; Table[T[k, n - k], {n, 0, 10}, {k, 0, n}] // Flatten (* Amiram Eldar, Aug 01 2020 *)
PROG
(PARI) {T(n, k) = if(n==0, 1, sum(j=1, n, (-2)^(n-j)*binomial(n, j)*binomial(n+(k-1)*j, j-1))/n)}
(PARI) {T(n, k) = local(A=1+x*O(x^n)); for(i=0, n, A=1+x*A^k/(1+2*x*A)); polcoef(A, n)}
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Seiichi Manyama, Aug 01 2020
STATUS
approved