login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A106823
Triangle read by rows: g.f. for row r is Product( (x^i-x^(r+1))/(1-x^i), i = 1..r-2).
2
1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 2, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 3, 3, 3, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 4, 4, 5, 4, 4, 3, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 4, 5, 6, 6, 6, 6, 5, 4, 3, 2, 1, 1
OFFSET
0,14
REFERENCES
See A008968 for references.
EXAMPLE
Initial rows are:
[1]
[1]
[1]
[0, 1, 1, 1, 1]
[0, 0, 0, 1, 1, 2, 2, 2, 1, 1]
[0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 3, 3, 3, 2, 1, 1]
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 4, 4, 5, 4, 4, 3, 2, 1, 1]
MAPLE
f3:=r->mul( (x^i-x^(r+1))/(1-x^i), i = 1..r-3); for r from 1 to 10 do series(f3(r), x, 50); od:
MATHEMATICA
f[n_, x_]:= Product[(x^j -x^(n+2))/(1-x^j), {j, n-2}];
T[n_]:= CoefficientList[f[n, x], x];
Table[T[n], {n, 0, 10}]//Flatten (* G. C. Greubel, Sep 14 2021 *)
CROSSREFS
If the initial zeros in each row are omitted, we get A008968.
Sequence in context: A112159 A058101 A132980 * A160096 A029446 A358479
KEYWORD
nonn,tabf
AUTHOR
N. J. A. Sloane, May 20 2005
STATUS
approved