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%I #15 Aug 23 2021 22:43:52
%S 0,2027025,10321920,34459425,92897280,218243025,464486400,916620705,
%T 1703116800,3011753745,5109350400,8365982625,13284311040,20534684625,
%U 30996725760,45808142625,66421555200,94670161425,132843110400,183771489825,250925875200,338526428625,451666575360
%N a(n) = n*(n+2)*(n+4)*(n+6)*(n+8)*(n+10)*(n+12)*(n+14).
%C a(n) can always be expressed as the difference of two squares: x^2 - y^2.
%C A346514(n) gives the x-values for each product. The y-values being A152691(n+7).
%C More generally, for any k, we have: n*(n+k)*(n+2*k)*...*(n+7*k) = a(n,k) = x(n,k)^2 - y(n,k)^2, where
%C x(n,k) = n^4 + 14*k*n^3 + 63*k^2*n^2 + 98*k^3*n + 28*k^4,
%C y(n,k) = 8*k^3*n + 28*k^4.
%C A239035(n) corresponds to a(n,k) in the case k = 1, with related y(n,k) = A346376(n).
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).
%F a(n) = A346514(n)^2 - A152691(n+7)^2.
%t a[n_] := (n + 14)!!/(n - 2)!!; Array[a, 23, 0] (* _Amiram Eldar_, Jul 22 2021 *)
%Y Cf. A239035, A190577, A346514, A346376.
%K nonn,easy
%O 0,2
%A _Lamine Ngom_, Jul 21 2021
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