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A170964
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Expansion of Product_{i=1..m} (1 + x^(4*i-1)) for m = 11.
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1
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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, 1, 0, 2, 3, 1, 0, 3, 4, 1, 1, 4, 4, 1, 1, 5, 5, 1, 2, 7, 5, 0, 3, 8, 5, 0, 5, 10, 4, 1, 6, 11, 4, 1, 9, 12, 3, 2, 11, 12, 3, 3, 14, 13, 2, 5, 16, 12, 2, 7, 19, 12, 2, 10, 20, 11, 2, 12, 23, 10, 2, 16, 23, 8, 3, 19, 24, 7, 5
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OFFSET
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0,19
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COMMENTS
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Product_{i=1..m} (1 + x^(4*i-1)) is the Poincaré polynomial for both Sp(2m) and O(2m+1).
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REFERENCES
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H. Weyl, The Classical Groups, Princeton, 1946, see p. 238.
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LINKS
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FORMULA
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MATHEMATICA
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CoefficientList[Series[Product[1+x^(4k-1), {k, 11}], {x, 0, 100}], x] (* Harvey P. Dale, Sep 19 2020 *)
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CROSSREFS
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KEYWORD
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nonn,fini,full,easy
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AUTHOR
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STATUS
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approved
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