OFFSET
0,43
COMMENTS
For n >= 1, row n is the Poincaré polynomial for the Lie group A_n.
Row sums are powers of 2.
REFERENCES
Borel, A. and Chevalley, C., The Betti numbers of the exceptional groups, Mem. Amer. Math. Soc. 1955, no. 14, pp 1-9.
Samuel I. Goldberg, Curvature and Homology, Dover, New York, 1998, page 144
LINKS
Alois P. Heinz, Rows n = 0..40, flattened
FORMULA
p(x,n) = Product[(1 + x^(2*k + 1)), {k, 1, n}]; t(n,m)=coefficients(p(x,n)).
EXAMPLE
Triangle begins:
{1} (the empty product)
{1, 0, 0, 1},
{1, 0, 0, 1, 0, 1, 0, 0, 1},
{1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1},
{1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 2, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1},
{1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 2, 0, 2, 1, 2, 1, 1, 2, 1, 2, 0, 2, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1},
...
MAPLE
A:=n->mul(1+x^(2*r+1), r=1..n);
for n from 1 to 12 do lprint(seriestolist(series(A(n), x, 10000))); od:
MATHEMATICA
Clear[p, x, n, m]; p[x_, n_] = Product[(1 + x^(2*k + 1)), {k, 1, n}]; Table[CoefficientList[p[x, n], x], {n, 1, 10}]; Flatten[%]
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Roger L. Bagula and Gary W. Adamson, Sep 26 2008
EXTENSIONS
Edited by N. J. A. Sloane, Dec 25 2010
STATUS
approved