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A173264 T(0,k) = 1 and T(n,k) = [x^k] ((x - 2)*x^n + 1)/((x - 1)*(x + 1)^n) for n >= 1, square array read by descending antidiagonals (n >= 0, k >= 0). 2
1, 1, -1, 1, 2, -1, 1, -2, 1, -1, 1, 2, 0, 2, -1, 1, -2, -1, -4, 3, -1, 1, 2, 2, 8, -7, 4, -1, 1, -2, -3, -14, 13, -11, 5, -1, 1, 2, 4, 22, -20, 24, -16, 6, -1, 1, -2, -5, -32, 27, -46, 40, -22, 7, -1, 1, 2, 6, 44, -33, 82, -86, 62, -29, 8, -1, 1, -2, -7, -58, 37, -139, 166, -148, 91, -37, 9, -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 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

Cf. A173265, A173266.

Sequence in context: A280747 A110955 A211983 * A056731 A042974 A235757

Adjacent sequences: A173261 A173262 A173263 * A173265 A173266 A173267

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 January 30 02:40 EST 2023. Contains 359939 sequences. (Running on oeis4.)