A144384 T(1,k) = 1 and T(n,k) = [t^k] (1 - t)/(1 - t^n) for n >= 2, square array read by ascending antidiagonals (n >= 1, k >= 0).

1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 0, -1, 1, 1, -1, 0, 1, 1, 1, 1, -1, 0, 0, -1, -1, 1, 1, -1, 0, 0, 1, 0, 1, 1, 1, -1, 0, 0, 0, -1, 1, -1, 1, 1, -1, 0, 0, 0, 1, 0, -1, 1, 1, 1, -1, 0, 0, 0, 0, -1, 0, 0, -1, 1, 1, -1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, -1, 0, 0, 0, 0, 0, -1, 0, -1, -1, -1, 1

Offset

1,1

Links

G. C. Greubel, Table of n, a(n) for the first 50 rows

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  1 -1  1 -1  1 -1  1 -1  1 ...
    3 | 1 -1  0  1 -1  0  1 -1  0  1 -1 ...
    4 | 1 -1  0  0  1 -1  0  0  1 -1  0 ...
    5 | 1 -1  0  0  0  1 -1  0  0  0  1 ...
    6 | 1 -1  0  0  0  0  1 -1  0  0  0 ...
    7 | 1 -1  0  0  0  0  0  1 -1  0  0 ...
    8 | 1 -1  0  0  0  0  0  0  1 -1  0 ...
    9 | 1 -1  0  0  0  0  0  0  0  1 -1 ...
   10 | 1 -1  0  0  0  0  0  0  0  0  1 ...
   ...

Mathematica

f[t_, n_] = If[n == 1, 1/(1 - t), (1 - t)/(1 - 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 - x)/(1 - 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 18 2019 */

Crossrefs

Cf. A144382, A144383.

Sequence in context: A114213 A108358 A267959 * A144475 A011758 A015088

Adjacent sequences: A144381 A144382 A144383 * A144385 A144386 A144387

Keyword

sign,tabl,easy

Author

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

Extensions

Edited by Franck Maminirina Ramaharo, Jan 21 2019

Status

approved