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%I #10 Mar 19 2022 09:45:00
%S 1,1,7,5,61,91,547,205,4921,7381,44287,33215,398581,597871,3587227,
%T 672605,32285041,48427561,290565367,217924025,2615088301,3922632451,
%U 23535794707,8825923015,211822152361,317733228541,1906399371247,1429799528435,17157594341221
%N a(n) = p(0,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(3) as in A327321.
%C a(n) is a strong divisibility sequence; i.e., gcd(a(h),a(k)) = a(gcd(h,k)).
%F a(2*n - 1) = A015518(2*n - 1). - _Vaclav Kotesovec_, Mar 19 2022
%e See Example in A327321.
%t c[poly_] := If[Head[poly] === Times, Times @@ DeleteCases[(#1 (Boole[MemberQ[#1, x] || MemberQ[#1, y] || MemberQ[#1, z]] &) /@Variables /@ #1 &)[List @@ poly], 0], poly];
%t r = Sqrt[3]; f[x_, n_] := c[Factor[Expand[(r x + r)^n - (r x - 1/r)^n]]];
%t Flatten[Table[CoefficientList[f[x, n], x], {n, 1, 12}]]; (* A327321 *)
%t Table[f[x, n] /. x -> 0, {n, 1, 30}] (* A329008 *)
%t Table[f[x, n] /. x -> 1, {n, 1, 30}] (* A329009 *)
%t Table[f[x, n] /. x -> 2, {n, 1, 30}] (* A329010 *)
%t (* _Peter J. C. Moses_, Nov 01 2019 *)
%t Numerator[CoefficientList[Normal[Series[1/((4 + x)*(4 - 3*x)), {x, 0, 30}]], x]] (* _Vaclav Kotesovec_, Mar 19 2022 *)
%Y Cf. A015518, A327321, A329009, A329010.
%K nonn
%O 1,3
%A _Clark Kimberling_, Nov 08 2019
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