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%I #18 Aug 28 2022 08:24:18
%S -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,
%T 0,-1,0,-1,1
%N 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.
%C 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.
%C 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
%D R. L. Griess, Jr., Twelve Sporadic Groups, Springer, 1998; see p. 169.
%o (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
%Y Cf. A008869, A178795.
%K sign,fini,full,easy
%O 0,15
%A _N. J. A. Sloane_, Dec 26 2010