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%I #15 Jan 30 2021 01:51:41
%S 3,14,52,78,133,248
%N Dimensions of the traditional Cartan exceptional group sequence A1, G2, F4, E6, E7, E8.
%F P(n) = Poincare-Polynomial(n) = Product_{m=1..n} (1 + t^A129766(m)); a(n) = Length(CoefficientList(P(n),t)) - 1.
%t a[0] = {1};
%t a[1] = {1, 5};
%t a[2] = {1, 5, 7, 11};
%t a[3] = {1, 4, 5, 7, 8, 11};
%t a[4] = {1, 5, 7, 9, 11, 13, 17};
%t a[5] = {1, 7, 11, 13, 17, 19, 23, 29};
%t b0 = Table[Length[CoefficientList[Expand[Product[(1 + t^(2*a[i][[n]] + 1)), {n, 1, Length[a[i]]}]], t]] - 1, {i, 0, 5}]
%Y Cf. A129766.
%K nonn,fini,full,uned
%O 1,1
%A _Roger L. Bagula_, May 17 2007
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