%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