This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A346515 #15 Aug 23 2021 22:43:52 %S A346515 0,2027025,10321920,34459425,92897280,218243025,464486400,916620705, %T A346515 1703116800,3011753745,5109350400,8365982625,13284311040,20534684625, %U A346515 30996725760,45808142625,66421555200,94670161425,132843110400,183771489825,250925875200,338526428625,451666575360 %N A346515 a(n) = n*(n+2)*(n+4)*(n+6)*(n+8)*(n+10)*(n+12)*(n+14). %C A346515 a(n) can always be expressed as the difference of two squares: x^2 - y^2. %C A346515 A346514(n) gives the x-values for each product. The y-values being A152691(n+7). %C A346515 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 A346515 x(n,k) = n^4 + 14*k*n^3 + 63*k^2*n^2 + 98*k^3*n + 28*k^4, %C A346515 y(n,k) = 8*k^3*n + 28*k^4. %C A346515 A239035(n) corresponds to a(n,k) in the case k = 1, with related y(n,k) = A346376(n). %H A346515 <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 A346515 a(n) = A346514(n)^2 - A152691(n+7)^2. %t A346515 a[n_] := (n + 14)!!/(n - 2)!!; Array[a, 23, 0] (* _Amiram Eldar_, Jul 22 2021 *) %Y A346515 Cf. A239035, A190577, A346514, A346376. %K A346515 nonn,easy %O A346515 0,2 %A A346515 _Lamine Ngom_, Jul 21 2021