%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