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 1 0 -1 2 -3 4 -5 6 ...
3 | -1 2 -4 8 -14 22 -32 44 -58 ...
4 | -1 3 -7 13 -20 27 -33 37 -38 ...
5 | -1 4 -11 24 -46 82 -139 226 -354 ...
6 | -1 5 -16 40 -86 166 -294 485 -754 ...
7 | -1 6 -22 62 -148 314 -610 1108 -1910 ...
8 | -1 7 -29 91 -239 553 -1163 2269 -4164 ...
...
MATHEMATICA
p[x_, n_] = If[n == 0, 1/(1 - x), (x^n - Sum[x^i, {i, 0, n - 1}])/( 1 + x)^n];
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 - 2)*x^n + 1)/((x - 1)*(x + 1)^n), 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
KEYWORD
AUTHOR
Roger L. Bagula, Feb 14 2010
EXTENSIONS
Edited by Franck Maminirina Ramaharo, Jan 23 2019
STATUS
approved