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Coefficients of polynomials of a prime like factor set (skip power): p(x,n)=Sum[x^i, {i, 0, (Prime[n] - 1)/2,2}]; q(n,n)=Sum[(-1)^i*x^i, {i, 0, (Prime[n] - 1)/2,2}]; t(x,n)=If[n == 0, 1, If[n == 1, x + 1, (x + 1)*p[x, n]*q[x, n]]].
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%I #2 Mar 30 2012 17:34:34

%S 1,1,1,1,1,2,2,1,1,1,1,2,2,3,3,4,4,3,3,2,2,1,1,1,1,2,2,3,3,4,4,5,5,4,

%T 4,3,3,2,2,1,1,1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,7,7,6,6,5,5,4,4,3,3,2,

%U 2,1,1

%N Coefficients of polynomials of a prime like factor set (skip power): p(x,n)=Sum[x^i, {i, 0, (Prime[n] - 1)/2,2}]; q(n,n)=Sum[(-1)^i*x^i, {i, 0, (Prime[n] - 1)/2,2}]; 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, 8, 32, 50, 128, 200, 242, 392, 512, 648,...}.

%F p(x,n)=Sum[x^i, {i, 0, (Prime[n] - 1)/2.2}];

%F q(n,n)=Sum[(-1)^i*x^i, {i, 0, (Prime[n] - 1)/2,2}];

%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, 2, 2, 1, 1},

%e {1, 1, 2, 2, 3, 3, 4, 4, 3, 3, 2, 2, 1, 1},

%e {1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 4, 4, 3, 3, 2, 2, 1, 1},

%e {1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 7, 7, 6, 6, 5, 5, 4, 4, 3, 3, 2, 2, 1, 1}

%t Clear[p, q, t, x, n];

%t p[x_, n_] := Sum[x^i, {i, 0, (Prime[n] - 1)/2, 2}];

%t q[x_, n_] := Sum[(-1)^i*x^i, {i, 0, (Prime[n] - 1)/2, 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, 2}];

%t Table[CoefficientList[ExpandAll[t[x, n]], x], {n, 0, 10, 2}];

%t Flatten[%]

%K nonn,tabl,uned

%O 0,6

%A _Roger L. Bagula_, Mar 08 2009