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 A239035 Product of 8 consecutive integers. a(n) = RisingFactorial(n, 8). 6
 0, 40320, 362880, 1814400, 6652800, 19958400, 51891840, 121080960, 259459200, 518918400, 980179200, 1764322560, 3047466240, 5079110400, 8204716800, 12893126400, 19769460480, 29654190720, 43609104000, 62990928000, 89513424000, 125318793600, 173059286400 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Vincent Thill, Nombres consécutifs et carrés, author's blog, Aug 03 2013 (consecutive numbers and squares). Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1). FORMULA a(n) = n*(n+1)*(n+2)*(n+3)*(n+4)*(n+5)*(n+6)*(n+7). a(n) = (n^4+14*n^3+63*n^2+98*n+28)^2 - (28+8*n)^2. (see Thill link). G.f.: 40320*x / (1-x)^9. - Colin Barker, Mar 09 2014 From Amiram Eldar, Mar 08 2022: (Start) Sum_{n>=1} 1/a(n) = 1/35280. Sum_{n>=1} (-1)^(n+1)/a(n) = 8*log(2)/315 - 1163/66150. (End) MATHEMATICA CoefficientList[Series[40320 x/(1 - x)^9, {x, 0, 30}], x] (* Vincenzo Librandi, Mar 11 2014 *) PROG (PARI) a(n) = prod(k=0, 7, n+k); (PARI) concat([0], Vec(40320*x/(1-x)^9 + O(x^100))) \\ Colin Barker, Mar 09 2014 (Magma) [(n^4+14*n^3+63*n^2+98*n+28)^2-(28+8*n)^2: n in [0..30]]; // Vincenzo Librandi, Mar 11 2014 (Sage) print([rising_factorial(n, 8) for n in range(23)]) # Peter Luschny, Mar 22 2022 CROSSREFS Cf. Product of n consecutive integers: A002378 (n=2), A007531 (n=3), A052762 (n=4), A052787 (n=5), A053625 (n=6), A159083 (n=7). Sequence in context: A321844 A226887 A284205 * A179734 A061123 A029576 Adjacent sequences: A239032 A239033 A239034 * A239036 A239037 A239038 KEYWORD nonn,easy AUTHOR Michel Marcus, Mar 09 2014 STATUS approved

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Last modified June 8 18:04 EDT 2023. Contains 363165 sequences. (Running on oeis4.)