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A144384
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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).
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3
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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
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OFFSET
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1,1
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LINKS
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EXAMPLE
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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 ...
...
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MATHEMATICA
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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}]]
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PROG
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(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);
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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