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A329007 a(n) = p(2,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(2) as in A327320.

%I A329007 #6 Nov 23 2019 13:40:30
%S A329007 1,9,21,405,2511,5103,92583,557685,372519,20135709,120873303,
%T A329007 241805655,4353033231,26119793709,52241181741,940355620245,
%U A329007 5642176768191,3761465527701,203119525916343,1218718317759525,2437437797780517,43873890820402509,263243376303474663
%N A329007 a(n) = p(2,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(2) as in A327320.
%C A329007 a(n) is a strong divisibility sequence; i.e., gcd(a(h),a(k)) = a(gcd(h,k)).
%e A329007 See Example in A327320.
%t A329007 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 A329007 r = Sqrt[2]; f[x_, n_] := c[Factor[Expand[(r x + r)^n - (r x - 1/r)^n]]];
%t A329007 Flatten[Table[CoefficientList[f[x, n], x], {n, 1, 12}]];  (* A327320 *)
%t A329007 Table[f[x, n] /. x -> 0, {n, 1, 30}]   (* A329005 *)
%t A329007 Table[f[x, n] /. x -> 1, {n, 1, 30}]   (* A329006 *)
%t A329007 Table[f[x, n] /. x -> 2, {n, 1, 30}]   (* A329007 *)
%t A329007 (* _Peter J. C. Moses_, Nov 01 2019 *)
%Y A329007 Cf. A327320, A329005, A329006.
%K A329007 nonn
%O A329007 1,2
%A A329007 _Clark Kimberling_, Nov 08 2019