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 A032780 a(n) = n(n+1)(n+2)...(n+8) / (n+(n+1)+(n+2)+...+(n+8)). 2
 0, 8064, 67200, 316800, 1108800, 3203200, 8072064, 18345600, 38438400, 75398400, 140025600, 248312064, 423259200, 697132800, 1114220800, 1734163200, 2635928064, 3922512000, 5726448000, 8216208000, 11603592000, 16152200064, 22187088000, 30105712000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 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 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) MATHEMATICA nn = 9; Table[c = Range[n, n + nn - 1]; Times @@ c/Total[c], {n, 0, 25}] (* T. D. Noe, Mar 18 2014 *) PROG (PARI) a(n) = prod(i=0, 8, n+i)/sum(i=0, 8, n+i); \\ Michel Marcus, Mar 18 2014 CROSSREFS Cf. A032765-A032798. Cf. A104678. Sequence in context: A157663 A232075 A109486 * A159224 A234446 A318104 Adjacent sequences: A032777 A032778 A032779 * A032781 A032782 A032783 KEYWORD nonn 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

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Last modified December 7 10:56 EST 2023. Contains 367650 sequences. (Running on oeis4.)