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A106822
Triangle read by rows: g.f. for row r is Product_{i=1..r-2} (x^i-x^(r+1))/(1-x^i).
3
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
OFFSET
0,12
REFERENCES
See A008967 for references.
EXAMPLE
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]
MAPLE
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:
MATHEMATICA
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 *)
PROG
(PARI) row(r) = Vecrev(prod(i=1, r-2, (x^i-x^(r+1))/(1-x^i))); \\ Michel Marcus, Sep 14 2021
CROSSREFS
If the initial zeros in each row are omitted, we get A008967.
Sequence in context: A053622 A016408 A316868 * A203905 A309142 A064532
KEYWORD
nonn,tabf
AUTHOR
N. J. A. Sloane, May 20 2005
STATUS
approved