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A144382 T(1,k) = -1 and T(n,k) = [t^k] 1/(-1 + t - t^n) for n >= 2, square array read by ascending antidiagonals (n >= 1, k >= 0). 2
-1, -1, -1, -1, -1, -1, -1, -1, 0, -1, -1, -1, -1, 1, -1, -1, -1, -1, 0, 1, -1, -1, -1, -1, -1, 1, 0, -1, -1, -1, -1, -1, 0, 2, -1, -1, -1, -1, -1, -1, -1, 1, 2, -1, -1, -1, -1, -1, -1, -1, 0, 2, 1, 0, -1, -1, -1, -1, -1, -1, -1, 1, 3, -1, 1, -1, -1, -1, -1, -1, -1, -1, 0, 2, 3, -3, 1, -1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,34

LINKS

Table of n, a(n) for n=1..78.

EXAMPLE

Array begins:

  n\k |  0  1  2  3  4  5  6  7  8  9 10 ...

  -------------------------------------------

    1 | -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 ...

    2 | -1 -1  0  1  1  0 -1 -1  0  1  1 ...

    3 | -1 -1 -1  0  1  2  2  1 -1 -3 -4 ...

    4 | -1 -1 -1 -1  0  1  2  3  3  2  0 ...

    5 | -1 -1 -1 -1 -1  0  1  2  3  4  4 ...

    6 | -1 -1 -1 -1 -1 -1  0  1  2  3  4 ...

    7 | -1 -1 -1 -1 -1 -1 -1  0  1  2  3 ...

    8 | -1 -1 -1 -1 -1 -1 -1 -1  0  1  2 ...

    9 | -1 -1 -1 -1 -1 -1 -1 -1 -1  0  1 ...

   10 | -1 -1 -1 -1 -1 -1 -1 -1 -1 -1  0 ...

   ...

MATHEMATICA

f[t_, n_] = If[n == 1, 1/(-1 + t), 1/(-1 + t - t^n)];

a = Table[Table[SeriesCoefficient[Series[f[t, m], {t, 0, 30}], n], {n, 0, 30}], {m, 1, 31}];

Flatten[Table[Table[a[[n - m + 1]][[m]], {m, 1, n }], {n, 1, 15}]]

PROG

(Maxima)(nn : 15, kk : 50)$

gf(n) := taylor(if n = 1 then 1/(1 - x) else  1/(-1 + x - x^n), x, 0, kk)$

T(n, k) := ratcoef(gf(n), x, k)$

create_list(T(n - k, k), n, 1, nn, k, 0, n - 1);

/* Franck Maminirina Ramaharo, Jan 21 2019 */

CROSSREFS

Cf. A144383, A144384.

Sequence in context: A037832 A170977 A039737 * A139553 A078379 A121657

Adjacent sequences:  A144379 A144380 A144381 * A144383 A144384 A144385

KEYWORD

sign,easy,tabl

AUTHOR

Roger L. Bagula and Gary W. Adamson, Oct 01 2008

EXTENSIONS

Edited by Franck Maminirina Ramaharo, Jan 21 2019

STATUS

approved

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Last modified October 27 06:31 EDT 2021. Contains 348271 sequences. (Running on oeis4.)