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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.

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%I A178725 #14 Dec 26 2023 10:20:18
%S A178725 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 A178725 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 A178725 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 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.
%C A178725 For n >= 1, row n is the Poincaré polynomial for the Lie group B_n (or, equally, Sp(2n) or O(2n+1)).
%C A178725 Row sums are powers of 2.
%D A178725 Borel, A. and Chevalley, C., The Betti numbers of the exceptional groups, Mem. Amer. Math. Soc. 1955, no. 14, pp 1-9.
%D A178725 H. Weyl, The Classical Groups, Princeton, 1946, see p. 238.
%e A178725 Triangle begins:
%e A178725 [1] (the empty product)
%e A178725 [1, 0, 0, 1]
%e A178725 [1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1]
%e A178725 [1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1]
%e A178725 [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 A178725 [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 A178725 ...
%Y A178725 Rows: A170956-A170965. Cf. A142724.
%K A178725 nonn,tabf
%O A178725 0,57
%A A178725 _N. J. A. Sloane_, Dec 26 2010