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A001095
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a(n) = n + n*(n-1)*(n-2)*(n-3)*(n-4).
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3
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0, 1, 2, 3, 4, 125, 726, 2527, 6728, 15129, 30250, 55451, 95052, 154453, 240254, 360375, 524176, 742577, 1028178, 1395379, 1860500, 2441901, 3160102, 4037903, 5100504, 6375625, 7893626, 9687627, 11793628, 14250629, 17100750, 20389351
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OFFSET
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0,3
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LINKS
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FORMULA
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G.f.: x*(1 - 4*x + 6*x^2 - 4*x^3 + 121*x^4)/(1-x)^6. - Colin Barker, Jun 25 2012
a(n) = n + 5!*binomial(n,5).
E.g.f.: x*(1 + x^4)*exp(x). (End)
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MAPLE
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seq(n + 5!*binomial(n, 5), n=0..35); # G. C. Greubel, Aug 26 2019
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MATHEMATICA
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Table[n+Times@@(n-Range[0, 4]), {n, 0, 40}] (* or *) LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, 1, 2, 3, 4, 125}, 40] (* Harvey P. Dale, Oct 08 2017 *)
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PROG
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(Magma) [n + n*(n-1)*(n-2)*(n-3)*(n-4): n in [0..35]]; // Vincenzo Librandi, Apr 30 2011
(PARI) vector(35, n, (n-1) + 5!*binomial(n-1, 5)) \\ G. C. Greubel, Aug 26 2019
(Sage) [n + 120*binomial(n, 5) for n in (0..35)] # G. C. Greubel, Aug 26 2019
(GAP) List([0..35], n-> n + 120*Binomial(n, 5)); # G. C. Greubel, Aug 26 2019
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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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EXTENSIONS
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STATUS
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approved
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