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A106822
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Triangle read by rows: g.f. for row r is Product_{i=1..r-2} (x^i-x^(r+1))/(1-x^i).
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3
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1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 2, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 3, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 3, 3, 3, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 3, 3, 4, 3, 3, 2, 2, 1
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OFFSET
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0,12
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REFERENCES
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LINKS
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EXAMPLE
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Initial rows are:
[1]
[1]
[0, 1, 1, 1]
[0, 0, 0, 1, 1, 2, 1, 1]
[0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 1, 1]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 3, 2, 2, 1, 1]
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MAPLE
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f2:=r->mul( (x^i-x^(r+1))/(1-x^i), i = 1..r-2); for r from 1 to 10 do series(f2(r), x, 50); od:
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MATHEMATICA
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f[n_, x_]:= Product[(x^j - x^(n+2))/(1 - x^j), {j, n-1}];
T[n_]:= CoefficientList[f[n, x], x];
Table[T[n], {n, 0, 10}]//Flatten (* G. C. Greubel, Sep 12 2021 *)
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PROG
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(PARI) row(r) = Vecrev(prod(i=1, r-2, (x^i-x^(r+1))/(1-x^i))); \\ Michel Marcus, Sep 14 2021
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CROSSREFS
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If the initial zeros in each row are omitted, we get A008967.
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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