OFFSET
0,2
COMMENTS
a(n) can always be expressed as the difference of two squares: x^2 - y^2.
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.
LINKS
Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).
MATHEMATICA
a[n_] := (n + 14)!!/(n - 2)!!; Array[a, 23, 0] (* Amiram Eldar, Jul 22 2021 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Lamine Ngom, Jul 21 2021
STATUS
approved