A032780 a(n) = n(n+1)(n+2)...(n+8) / (n+(n+1)+(n+2)+...+(n+8)).

0, 8064, 67200, 316800, 1108800, 3203200, 8072064, 18345600, 38438400, 75398400, 140025600, 248312064, 423259200, 697132800, 1114220800, 1734163200, 2635928064, 3922512000, 5726448000, 8216208000, 11603592000, 16152200064, 22187088000, 30105712000

Offset: 0

Author

Patrick De Geest, May 15 1998

Keywords

• nonn

Comments

a(5n+1) == 4 modulo 10.

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

Crossrefs

Cf. A032765-A032798.

Cf. A104678.

Programs

Mathematica

nn = 9; Table[c = Range[n, n + nn - 1]; Times @@ c/Total[c], {n, 0, 25}] (* T. D. Noe, Mar 18 2014 *)

PARI

a(n) = prod(i=0, 8, n+i)/sum(i=0, 8, n+i); \\ Michel Marcus, Mar 18 2014

Formula

a(-n) = a(n-8) for all n in Z. - Michael Somos, Mar 18 2014

a(n) = 64 * A104678(n-1) = 64 * binomial(n+3, 4) * binomial(n+8, 4). - Michael Somos, Mar 18 2014

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)

Extensions

Typo in name fixed by Zak Seidov, Mar 18 2014

More terms from Michel Marcus, Mar 18 2014