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 A346515 a(n) = n*(n+2)*(n+4)*(n+6)*(n+8)*(n+10)*(n+12)*(n+14). 1
 0, 2027025, 10321920, 34459425, 92897280, 218243025, 464486400, 916620705, 1703116800, 3011753745, 5109350400, 8365982625, 13284311040, 20534684625, 30996725760, 45808142625, 66421555200, 94670161425, 132843110400, 183771489825, 250925875200, 338526428625, 451666575360 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(n) can always be expressed as the difference of two squares: x^2 - y^2. A346514(n) gives the x-values for each product. The y-values being A152691(n+7). 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   x(n,k) = n^4 + 14*k*n^3 + 63*k^2*n^2 + 98*k^3*n + 28*k^4,   y(n,k) = 8*k^3*n + 28*k^4. A239035(n) corresponds to a(n,k) in the case k = 1, with related y(n,k) = A346376(n). LINKS Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1). FORMULA a(n) = A346514(n)^2 - A152691(n+7)^2. MATHEMATICA a[n_] := (n + 14)!!/(n - 2)!!; Array[a, 23, 0] (* Amiram Eldar, Jul 22 2021 *) CROSSREFS Cf. A239035, A190577, A346514, A346376. Sequence in context: A032754 A271768 A104441 * A290037 A289956 A263892 Adjacent sequences:  A346512 A346513 A346514 * A346516 A346517 A346518 KEYWORD nonn,easy AUTHOR Lamine Ngom, Jul 21 2021 STATUS approved

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Last modified December 6 22:42 EST 2021. Contains 349567 sequences. (Running on oeis4.)