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A152726
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a(n) = n^7 - (n-1)^7 + (n-2)^7 - ... + ((-1)^n)*0^7.
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10
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0, 1, 127, 2060, 14324, 63801, 216135, 607408, 1489744, 3293225, 6706775, 12780396, 23051412, 39697105, 65716399, 105142976, 163292480, 247046193, 365173839, 528697900, 751302100, 1049786441, 1444571447, 1960254000
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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 + 120*x + 1191*x^2 + 2416*x^3 + 1191*x^4 + 120*x^5 + x^6)/((1+x)*(x-1)^8). - R. J. Mathar, Jul 08 2013
a(n) = (17*(-1)^n + 84*n^2 - 17 + 28*n^6 + 8*n^7 - 70*n^4)/16. - R. J. Mathar, Jul 08 2013
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MATHEMATICA
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k=0; lst={k}; Do[k=n^7-k; AppendTo[lst, k], {n, 1, 5!}]; lst
LinearRecurrence[{7, -20, 28, -14, -14, 28, -20, 7, -1}, {0, 1, 127, 2060, 14324, 63801, 216135, 607408, 1489744}, 50] (* G. C. Greubel, Sep 01 2018 *)
Table[Total[(Times@@@Partition[Riffle[Range[n, 1, -1], {1, -1}, {2, -1, 2}], 2])^7], {n, 0, 30}] (* Harvey P. Dale, Mar 14 2023 *)
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PROG
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(PARI) x='x+O('x^50); concat([0], Vec(x*(1+120*x+1191*x^2 +2416*x^3 +1191*x^4+120*x^5+x^6)/((1+x)*(x-1)^8))) \\ G. C. Greubel, Sep 01 2018
(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!(x*(1+120*x+1191*x^2+2416*x^3+1191*x^4 +120*x^5+x^6)/( (1+x)*(x-1)^8))); // G. C. Greubel, Sep 01 2018
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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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