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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: A079066 A157188 A329257 * A342149 A224326 A096496

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 November 29 11:46 EST 2022. Contains 358424 sequences. (Running on oeis4.)