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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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..77.

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

Cf. A173264, A173265.

Sequence in context: A109066 A079066 A157188 * A224326 A096496 A117209

Adjacent sequences:  A173263 A173264 A173265 * A173267 A173268 A173269

KEYWORD

sign,easy,tabl

AUTHOR

Roger L. Bagula, Feb 14 2010

EXTENSIONS

Edited by Franck Maminirina Ramaharo, Jan 23 2019

STATUS

approved

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Last modified May 23 06:57 EDT 2019. Contains 323508 sequences. (Running on oeis4.)