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 A142724 Irregular triangle read by rows: row n gives coefficients in expansion of Product_{k=1..n} (1 + x^(2*k + 1)) for n >= 0. 14
 1, 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, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 2, 1, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,43 COMMENTS For n >= 1, row n is the PoincarĂ© 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 Cf. A178600, A178602, A178580, A178651, A178665, A178666. Rows: A178686. A178687, A178691, A178692, A178695, A178696, A178697. Sequence in context: A184159 A231122 A178686 * A174656 A178798 A318277 Adjacent sequences:  A142721 A142722 A142723 * A142725 A142726 A142727 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

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Last modified August 2 17:02 EDT 2021. Contains 346428 sequences. (Running on oeis4.)