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Expansion of the polynomial (1+x^3)*(1+x^11)*(1+x^15)*(1+x^19)*(1+x^23)*(1+x^27)*(1+x^35)
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%I #11 Jul 19 2015 10:49:54

%S 1,0,0,1,0,0,0,0,0,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,2,1,0,1,2,0,0,1,

%T 2,1,0,2,3,0,0,2,2,0,0,3,2,0,1,3,2,0,1,4,1,0,2,3,1,0,2,4,1,0,3,3,0,0,

%U 3,3,0,1,4,2,0,1,3,2,0,1,4,1,0,2,3,1,0,2,3,0,0,2,2,0,0,3,2,0,1,2,1,0,0,2,1,0,1,2,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,0,0,0,0,0,1,0,0,1

%N Expansion of the polynomial (1+x^3)*(1+x^11)*(1+x^15)*(1+x^19)*(1+x^23)*(1+x^27)*(1+x^35)

%C This is the Poincaré polynomial for the Lie group E_7.

%D Borel, A. and Chevalley, C., The Betti numbers of the exceptional groups, Mem. Amer. Math. Soc. 1955, no. 14, pp 1-9.

%t CoefficientList[Series[(1+x^3)(1+x^11)(1+x^15)(1+x^19)(1+x^23)(1+x^27)(1+x^35),{x,0,140}],x] (* _Harvey P. Dale_, Oct 12 2014 *)

%K nonn,fini,full,easy

%O 0,27

%A _N. J. A. Sloane_, Dec 24 2010