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Expansion of (Product_{i=1..m-1} (1 + x^(4*i-1))) * (1 + x^(2*m-1)) for m = 7.
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%I #20 Jan 04 2021 04:48:44

%S 1,0,0,1,0,0,0,1,0,0,1,1,0,1,1,1,1,0,2,1,1,1,2,2,1,1,3,1,1,2,2,2,1,3,

%T 3,2,2,3,2,3,1,3,3,2,2,3,3,2,2,3,3,1,3,2,3,2,2,3,3,1,2,2,2,1,1,3,1,1,

%U 2,2,1,1,1,2,0,1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0,1

%N Expansion of (Product_{i=1..m-1} (1 + x^(4*i-1))) * (1 + x^(2*m-1)) for m = 7.

%C (Product_{i=1..m-1} (1 + x^(4*i-1))) * (1 + x^(2*m-1)) is the Poincaré polynomial for O(2m).

%D H. Weyl, The Classical Groups, Princeton, 1946, see p. 238.

%t CoefficientList[Series[Product[1+x^(4i-1),{i,6}]*(1+x^13),{x,0,100}],x] (* _Harvey P. Dale_, Aug 24 2012 *)

%K nonn,fini,full

%O 0,19

%A _N. J. A. Sloane_, Aug 29 2010