A173266 T(0,k) = 1 and T(n,k) = [x^k] (x^(n + 1) - 1)/((x - 2)*x^n + 1) for n >= 1, square array read by descending antidiagonals (n >= 0, k >= 0).

1, 1, -1, 1, -2, -1, 1, -2, 0, -1, 1, -2, -2, 0, -1, 1, -2, 2, 0, 0, -1, 1, -2, -4, -2, 0, 0, -1, 1, -2, 6, 2, 0, 0, 0, -1, 1, -2, -10, 0, -2, 0, 0, 0, -1, 1, -2, 16, -4, 2, 0, 0, 0, 0, -1, 1, -2, -26, 6, 0, -2, 0, 0, 0, 0, -1, 1, -2, 42, -2, 0, 2, 0, 0, 0, 0, 0, -1

Offset: 0

Author

Roger L. Bagula, Feb 14 2010

Keywords

• sign
• easy
• tabl

Examples

			Square array begins:
  n\k |  0   1   2   3   4   5   6   7   8 ...
  --------------------------------------------
    0 |  1   1   1   1   1   1   1   1   1 ...
    1 | -1  -2  -2  -2  -2  -2  -2  -2  -2 ...
    2 | -1   0  -2   2  -4   6 -10  16 -26 ...
    3 | -1   0   0  -2   2   0  -4   6  -2 ...
    4 | -1   0   0   0  -2   2   0   0  -4 ...
    5 | -1   0   0   0   0  -2   2   0   0 ...
    6 | -1   0   0   0   0   0  -2   2   0 ...
    7 | -1   0   0   0   0   0   0  -2   2 ...
    8 | -1   0   0   0   0   0   0   0  -2 ...
    ...
		

Crossrefs

Cf. A173264, A173265.

Programs

Mathematica

p[x_, n_] = If[n == 0, 1/(1 - x), (Sum[x^i, {i, 0, n}])/(x^n - Sum[x^i, {i, 0, n - 1}])];
a = Table[Table[SeriesCoefficient[Series[p[x, n], {x, 0, 50}], m], {m, 0, 20}], {n, 0, 20}];
Flatten[Table[Table[a[[m, n - m + 1]], {m, 1, n}], {n, 1, 10}]]

Maxima

(kk : 50, nn : 15)$
gf(n) := taylor(if n = 0 then 1/(1 - x) else (x^(n + 1) - 1)/((x - 2)*x^n + 1), x, 0, kk)$
T(n, k) := ratcoef(gf(n), x, k)$
create_list(T(k, n - k), n, 0, nn, k, 0, n);
/* Franck Maminirina Ramaharo, Jan 23 2019 */

Extensions

Edited by Franck Maminirina Ramaharo, Jan 23 2019