%I
%S 1,1,0,0,1,1,0,0,1,0,0,0,1,0,0,1,1,0,0,1,0,0,0,1,0,0,1,1,0,0,1,0,0,0,
%T 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,
%U 0,0,0,1,0,0,1,1,0,0,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0,2,1,0,1,2,0,0,1,2,0,0,2,1,0,0,2,1,0,1,2,0,0,1,1,0,0,1,1,0,0,1,0,0,0,1,0,0,1,1,0,0,1,0,0,0,1,0,0,1,1,0,0,1,1,0,0,2,1,0,1,2,1,0,1,3,0,0,2,2,0,0,3,2,0,1,3,1,0,1,3,1,0,2,3,0,0,2,2,0,0,3,1,0,1,2,1,0,1,2,0,0,1,1,0,0,1,1,0,0,1,0,0,0,1,0,0,1
%N Irregular triangle read by rows: row n gives coefficients in expansion of Product_{k=1..n} (1 + x^(4*k  1) for n >= 0.
%C For n >= 1, row n is the PoincarĂ© polynomial for the Lie group B_n (or, equally, Sp(2n) or O(2n+1)).
%C Row sums are powers of 2.
%D Borel, A. and Chevalley, C., The Betti numbers of the exceptional groups, Mem. Amer. Math. Soc. 1955, no. 14, pp 19.
%D H. Weyl, The Classical Groups, Princeton, 1946, see p. 238.
%e Triangle begins:
%e [1] (the empty product)
%e [1, 0, 0, 1]
%e [1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1]
%e [1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1]
%e [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]
%e [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]
%e ...
%Y Rows: A170956A170965. Cf. A142724.
%K nonn,tabf
%O 0,57
%A _N. J. A. Sloane_, Dec 26 2010
