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%I #17 Jan 22 2019 08:47:28
%S 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,
%T 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,
%U -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
%N 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).
%H G. C. Greubel, <a href="/A144384/b144384.txt">Table of n, a(n) for the first 50 rows</a>
%e Array begins:
%e n\k | 0 1 2 3 4 5 6 7 8 9 10 ...
%e -----------------------------------------
%e 1 | 1 1 1 1 1 1 1 1 1 1 1 ...
%e 2 | 1 -1 1 -1 1 -1 1 -1 1 -1 1 ...
%e 3 | 1 -1 0 1 -1 0 1 -1 0 1 -1 ...
%e 4 | 1 -1 0 0 1 -1 0 0 1 -1 0 ...
%e 5 | 1 -1 0 0 0 1 -1 0 0 0 1 ...
%e 6 | 1 -1 0 0 0 0 1 -1 0 0 0 ...
%e 7 | 1 -1 0 0 0 0 0 1 -1 0 0 ...
%e 8 | 1 -1 0 0 0 0 0 0 1 -1 0 ...
%e 9 | 1 -1 0 0 0 0 0 0 0 1 -1 ...
%e 10 | 1 -1 0 0 0 0 0 0 0 0 1 ...
%e ...
%t f[t_, n_] = If[n == 1, 1/(1 - t), (1 - t)/(1 - t^n)];
%t a = Table[Table[SeriesCoefficient[Series[f[t, m], {t, 0, 30}], n], {n, 0, 30}], {m, 1, 31}];
%t Flatten[Table[Table[a[[n - m + 1]][[m]], {m, 1, n }], {n, 1, 15}]]
%o (Maxima)(nn : 15, kk : 50)$
%o gf(n) := taylor(if n = 1 then 1/(1 - x) else (1 - x)/(1 - x^n), x, 0, kk)$
%o T(n,k) := ratcoef(gf(n), x, k)$
%o create_list(T(n - k, k), n, 1, nn, k, 0, n - 1);
%o /* _Franck Maminirina Ramaharo_, Jan 18 2019 */
%Y Cf. A144382, A144383.
%K sign,tabl,easy
%O 1,1
%A _Roger L. Bagula_ and _Gary W. Adamson_, Oct 01 2008
%E Edited by _Franck Maminirina Ramaharo_, Jan 21 2019
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