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A178781
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Expansion of the polynomial (x^9-1)*(x^7-1)*(x^6-1)*(x^5-1)*(x^4-1)*(x^3-1)*(x-1) in increasing powers of x.
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3
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-1, 1, 0, 1, 0, 0, 0, -1, -1, 0, -1, 0, 1, 0, 2, 0, 1, 0, 0, -1, 0, -2, 0, -1, 0, 1, 0, 1, 1, 0, 0, 0, -1, 0, -1, 1
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OFFSET
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0,15
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COMMENTS
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q^63*(q^18-1)*(q^14-1)*(q^12-1)*(q^10-1)*(q^8-1)*(q^6-1)*(q^2-1) is the order of the simple group E_7(q), if q is a prime power.
The x-polynomial f(x) and the q-polynomial g(q) are such that g(q) = q^63*f(q^2) - Jean-François Alcover, Aug 25 2022
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REFERENCES
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R. L. Griess, Jr., Twelve Sporadic Groups, Springer, 1998; see p. 169.
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LINKS
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PROG
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(PARI) Vecrev((x^9-1)*(x^7-1)*(x^6-1)*(x^5-1)*(x^4-1)*(x^3-1)*(x-1)) \\ Michel Marcus, Aug 25 2022
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CROSSREFS
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KEYWORD
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sign,fini,full,easy
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AUTHOR
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STATUS
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approved
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