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%I #20 Aug 28 2022 08:25:59
%S 1,-1,0,0,-1,1,-1,0,1,-1,1,1,-2,3,-1,-1,3,-3,1,1,-4,3,-1,-3,4,-4,1,3,
%T -5,4,0,-3,6,-3,0,4,-5,3,1,-4,4,-3,-1,3,-4,1,1,-3,3,-1,-1,3,-2,1,1,-1,
%U 1,0,-1,1,-1,0,0,-1,1
%N Expansion of the polynomial (x^15-1)*(x^12-1)*(x^10-1)*(x^9-1)*(x^7-1)*(x^6-1)*(x^4-1)*(x-1) in increasing powers of x.
%C q^120*(q^30-1)*(q^24-1)*(q^20-1)*(q^18-1)*(q^14-1)*(q^12-1)*(q^8-1)*(q^2-1) is the order of the simple group E_8(q), if q is a prime power.
%C If f(x) is the x-polynomial and g(q) the q-polynomial, then g(q) = q^120*f(q^2). - _Jean-François Alcover_, Aug 25 2022
%D R. L. Griess, Jr., Twelve Sporadic Groups, Springer, 1998; see p. 169.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/E8_(mathematics)">Lie group E8</a>
%e With p=2 one gets the order of E_8(2): 337804753143634806261388190614085595079991692242467651576160959909068800000. - _Jean-François Alcover_, Aug 25 2022
%o (PARI) Vec((x^15-1)*(x^12-1)*(x^10-1)*(x^9-1)*(x^7-1)*(x^6-1)*(x^4-1)*(x-1)) \\ _Michel Marcus_, Aug 25 2022
%Y Cf. A009968, A178779, A178780, A178781.
%K sign,fini,full
%O 0,13
%A _N. J. A. Sloane_, Dec 26 2010
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