OFFSET
0,57
COMMENTS
For n >= 1, row n is the Poincaré polynomial for the Lie group B_n (or, equally, Sp(2n) or O(2n+1)).
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.
H. Weyl, The Classical Groups, Princeton, 1946, see p. 238.
EXAMPLE
Triangle begins:
[1] (the empty product)
[1, 0, 0, 1]
[1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1]
[1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1]
[1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 2, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1]
[1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 2, 1, 0, 1, 2, 0, 0, 1, 2, 0, 0, 2, 1, 0, 0, 2, 1, 0, 1, 2, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1]
...
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
N. J. A. Sloane, Dec 26 2010
STATUS
approved