%I A143479
%S A143479 1,22,263,2284,16225,100490,564096,2943434,14525316,68623698,313160381,
%T A143479 1389603972,6026265844,25641735564,107383041717,443700335414,1812509085585,
%U A143479 7331932395596,29409752732192,117108140185676,463355891177610,1823137506023896
%V A143479 -1,-22,-263,-2284,-16225,-100490,-564096,-2943434,-14525316,-68623698,
               -313160381,
%W A143479 -1389603972,-6026265844,-25641735564,-107383041717,-443700335414,-1812509085585,
%X A143479 -7331932395596,-29409752732192,-117108140185676,-463355891177610,-1823137506023896
%N A143479 Coefficient expansion of the McMullen transformed characteristic polynomial 
               of the E_11 Cartan Matix: p(x)]=-2 - 167 x + 1694 x^2 - 6069 x^3 
               + 11210 x^4 - 12297 x^5 + 8554 x^6 -3875 x^7 + 1140 x^8 - 210 x^9 
               + 22 x^10 - x^11.
%C A143479 The polynomial is symmetric:
%C A143479 h[x]=x^22*h[1/x].
%C A143479 It would be fairly easy to map the McMullem 22nd degree
%C A143479 Salem which is related to K3 dynamics (and a tetrahedral surface) to 
               this 22nd degree polynomial. The McMullen Salem polynomial has the 
               ratio of
%C A143479 1.3728862806447408 which is near 1/(100*Alpha) the fine structure constyant.
%F A143479 p(x)]=-2 - 167 x + 1694 x^2 - 6069 x^3 + 11210 x^4 - 12297 x^5 + 8554 
               x^6 -3875 x^7 + 1140 x^8 - 210 x^9 + 22 x^10 - x^11; q(x)=x^11*p(x+1/
               x); a(n)=Coefficient_Expansion(q(x)).
%t A143479 m11 = {{2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {-1, 2, -1, 0, 0, 0, 0, 0, 
               0, 0, 0}, {0, -1, 2, -1, 0, 0, 0, 0, 0, 0, -1}, {0, 0, -1, 2, -1, 
               0, 0, 0, 0, 0, 0}, {0, 0, 0, -1, 2, -1, 0, 0, 0, 0, 0}, {0, 0, 0, 
               0, -1, 2, -1, 0, 0, 0, 0}, {0, 0, 0, 0, 0, -1, 2, -1, 0, 0, 0}, {0, 
               0, 0, 0, 0, 0, -1, 2, -1, 0, 0}, {0, 0, 0, 0, 0, 0, 0, -1, 2, -1, 
               0}, {0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 0}, {0, 0, -1, 0, 0, 0, 0, 0, 
               0, 0, 2}}; f[x_] = CharacteristicPolynomial[m11, x]; h[x_] = ExpandAll[x^11*f[x 
               + 1/x]]; g[x] = ExpandAll[x^22*h[1/x]]; a = Table[SeriesCoefficient[Series[1/
               g[x], {x, 0, 30}], n], {n, 0, 30}]
%Y A143479 Sequence in context: A028571 A010974 A022587 this_sequence A004412 A055756 
               A128766
%Y A143479 Adjacent sequences: A143476 A143477 A143478 this_sequence A143480 A143481 
               A143482
%K A143479 uned,probation,sign
%O A143479 1,2
%A A143479 Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Oct 
               24 2008