OFFSET
0,2
COMMENTS
The product of any k consecutive integers is divisible by the sum of the same k integers for odd nonprime k's: 1 (trivial case), 9 (this sequence), 15, etc. - Zak Seidov, Mar 18 2014
LINKS
T. D. Noe, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).
FORMULA
a(5n+1) == 4 modulo 10.
From Michael Somos, Mar 18 2014: (Start)
a(-n) = a(n-8) for all n in Z.
a(n) = 64 * A104678(n-1) = 64 * binomial(n+3, 4) * binomial(n+8, 4). (End)
From Chai Wah Wu, Dec 17 2016: (Start)
a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n > 8.
G.f.: 64*x*(-x^4 + 9*x^3 - 36*x^2 + 84*x - 126)/(x - 1)^9. (End)
From Amiram Eldar, Oct 15 2025: (Start)
Sum_{n>=1} 1/a(n) = 9/62720.
Sum_{n>=1} (-1)^(n+1)/a(n) = 1/8960. (End)
MATHEMATICA
nn = 9; Table[c = Range[n, n + nn - 1]; Times @@ c/Total[c], {n, 0, 25}] (* T. D. Noe, Mar 18 2014 *)
With[{c=n+Range[0, 8]}, Table[Times@@c/Total[c], {n, 0, 30}]] (* Harvey P. Dale, May 15 2026 *)
PROG
(PARI) a(n) = prod(i=0, 8, n+i)/sum(i=0, 8, n+i); \\ Michel Marcus, Mar 18 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Patrick De Geest, May 15 1998
EXTENSIONS
Typo in name fixed by Zak Seidov, Mar 18 2014
More terms from Michel Marcus, Mar 18 2014
STATUS
approved