%I #5 Dec 27 2019 16:33:50
%S 1,17,229,2873,35101,424337,729667,61370153,736832461,8843942657,
%T 106137077509,1273693758233,15284569239421,26202293082311,
%U 2200998722429749,26412015186735113,316944334828711981,3803332780883996897,45639997185305228389,547679985297149068793
%N a(n) = p(1,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(6) as in A327323.
%C a(n) is a strong divisibility sequence; i.e., gcd(a(h),a(k)) = a(gcd(h,k)).
%e See Example in A327323.
%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[6]; 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}]]; (* A327323 *)
%t Table[f[x, n] /. x -> 0, {n, 1, 30}] (* A329014 *)
%t Table[f[x, n] /. x -> 1, {n, 1, 30}] (* A329015 *)
%t Table[f[x, n] /. x -> 2, {n, 1, 30}] (* A329016 *)
%t (* _Peter J. C. Moses_, Nov 01 2019 *)
%Y Cf. A327323, A329014, A329016.
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, Nov 23 2019