A106822 Triangle read by rows: g.f. for row r is Product_{i=1..r-2} (x^i-x^(r+1))/(1-x^i).

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

Author

N. J. A. Sloane, May 20 2005

Keywords

• nonn
• tabf

Examples

			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]
		

References

• See A008967 for references.

Links

• G. C. Greubel, Rows n = 0..25 of the irregular triangle, flattened

Crossrefs

If the initial zeros in each row are omitted, we get A008967.

Cf. A008967, A106823.

Programs

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 *)

PARI

row(r) = Vecrev(prod(i=1, r-2, (x^i-x^(r+1))/(1-x^i))); \\ Michel Marcus, Sep 14 2021