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A239035
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Product of 8 consecutive integers. a(n) = RisingFactorial(n, 8).
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6
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0, 40320, 362880, 1814400, 6652800, 19958400, 51891840, 121080960, 259459200, 518918400, 980179200, 1764322560, 3047466240, 5079110400, 8204716800, 12893126400, 19769460480, 29654190720, 43609104000, 62990928000, 89513424000, 125318793600, 173059286400
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OFFSET
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0,2
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LINKS
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FORMULA
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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).
Sum_{n>=1} 1/a(n) = 1/35280.
Sum_{n>=1} (-1)^(n+1)/a(n) = 8*log(2)/315 - 1163/66150. (End)
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MATHEMATICA
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CoefficientList[Series[40320 x/(1 - x)^9, {x, 0, 30}], x] (* Vincenzo Librandi, Mar 11 2014 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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