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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). 3

%I

%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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Last modified November 30 05:12 EST 2021. Contains 349419 sequences. (Running on oeis4.)