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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).
2
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
0,5
EXAMPLE
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 ...
...
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}]]
PROG
(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 */
CROSSREFS
Sequence in context: A079066 A157188 A329257 * A342149 A224326 A096496
KEYWORD
sign,easy,tabl
AUTHOR
Roger L. Bagula, Feb 14 2010
EXTENSIONS
Edited by Franck Maminirina Ramaharo, Jan 23 2019
STATUS
approved