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%I #2 Mar 30 2012 17:34:34
%S 1,1,1,1,1,-1,-1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,1,1,-1,-1,-1,
%T -1,-1,-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
%U 1,1,1,1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1
%N Coefficients of polynomials of a prime like factor set : p(x,n)=Sum[x^i, {i, 0, (Prime[n] - 1)/2}]; q(n,n)=Sum[(-1)^i*x^i, {i, 0, (Prime[n] - 1)/2}]; t(x,n)=If[n == 0, 1, If[n == 1, x + 1, (x + 1)*p[x, n]*q[x, n]]].
%C Row sums are:
%C {1, 2, 0, 6, 0, 0, 14, 18, 0, 0, 30, 0, 38, 42, 0, 0, 54, 0, 62, 0, 0,...}.
%C This row sum minus one picks out as cyclotomic the primes; A002144:
%C {5,13,17,29,37,41,53,61,...}
%F p(x,n)=Sum[x^i, {i, 0, (Prime[n] - 1)/2}];
%F q(n,n)=Sum[(-1)^i*x^i, {i, 0, (Prime[n] - 1)/2}];
%F t(x,n)=If[n == 0, 1, If[n == 1, x + 1, (x + 1)*p[x, n]*q[x, n]]];
%F out_(n,m)=coefficients(t(x,n)).
%e {1},
%e {1, 1},
%e {1, 1, -1, -1},
%e {1, 1, 1, 1, 1, 1},
%e {1, 1, 1, 1, -1, -1, -1, -1},
%e {1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1},
%e {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1},
%e {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1},
%e {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
%e {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1},
%e {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}
%t Clear[p, q, t, x, n];
%t p[x_, n_] := Sum[x^i, {i, 0, (Prime[n] - 1)/2}];
%t q[x_, n_] := Sum[(-1)^i*x^i, {i, 0, (Prime[n] - 1)/2}];
%t t[x_, n_] := If[n == 0, 1, If[n == 1, x + 1, (x + 1)*p[x, n]*q[x, n]]];
%t Table[ExpandAll[t[x, n]], {n, 0, 10}];
%t Table[CoefficientList[ExpandAll[t[x, n]], x], {n, 0, 10}];
%t Flatten[%]
%K sign,tabl,uned
%O 0,1
%A _Roger L. Bagula_, Mar 08 2009
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