cp's OEIS Frontend

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

%I A032780 #18 Dec 17 2016 17:29:48
%S A032780 0,8064,67200,316800,1108800,3203200,8072064,18345600,38438400,
%T A032780 75398400,140025600,248312064,423259200,697132800,1114220800,
%U A032780 1734163200,2635928064,3922512000,5726448000,8216208000,11603592000,16152200064,22187088000,30105712000
%N A032780 a(n) = n(n+1)(n+2)...(n+8) / (n+(n+1)+(n+2)+...+(n+8)).
%C A032780 a(5n+1) == 4 modulo 10.
%C A032780 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
%H A032780 T. D. Noe, <a href="/A032780/b032780.txt">Table of n, a(n) for n = 0..1000</a>
%F A032780 a(-n) = a(n-8) for all n in Z. - _Michael Somos_, Mar 18 2014
%F A032780 a(n) = 64 * A104678(n-1) = 64 * binomial(n+3, 4) * binomial(n+8, 4). - _Michael Somos_, Mar 18 2014
%F A032780 From _Chai Wah Wu_, Dec 17 2016: (Start)
%F A032780 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.
%F A032780 G.f.: 64*x*(-x^4 + 9*x^3 - 36*x^2 + 84*x - 126)/(x - 1)^9. (End)
%t A032780 nn = 9; Table[c = Range[n, n + nn - 1]; Times @@ c/Total[c], {n, 0, 25}] (* _T. D. Noe_, Mar 18 2014 *)
%o A032780 (PARI) a(n) = prod(i=0, 8, n+i)/sum(i=0, 8, n+i); \\ _Michel Marcus_, Mar 18 2014
%Y A032780 Cf. A032765-A032798.
%Y A032780 Cf. A104678.
%K A032780 nonn
%O A032780 0,2
%A A032780 _Patrick De Geest_, May 15 1998
%E A032780 Typo in name fixed by _Zak Seidov_, Mar 18 2014
%E A032780 More terms from _Michel Marcus_, Mar 18 2014