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 A178725 Irregular triangle read by rows: row n gives coefficients in expansion of Product_{k=1..n} (1 + x^(4*k - 1) for n >= 0. 0

%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 1-9.

%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: A170956-A170965. Cf. A142724.

%K nonn,tabf

%O 0,57

%A _N. J. A. Sloane_, Dec 26 2010

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Last modified August 4 21:32 EDT 2021. Contains 346455 sequences. (Running on oeis4.)