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A104682
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a(n) = Sum_{j=0..14} n^j.
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8
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1, 15, 32767, 7174453, 357913941, 7629394531, 94036996915, 791260251657, 5026338869833, 25736391511831, 111111111111111, 417724816941565, 1400638324962397, 4265491084507563, 11966776581370171, 31278135027204241, 76861433640456465, 178901440719363487
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OFFSET
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0,2
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (15,-105,455,-1365,3003,-5005,6435,-6435,5005,-3003,1365,-455,105,-15,1).
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FORMULA
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a(n) = n^14 + n^13 + n^12 + n^11 + n^10 + n^9 + n^8 + n^7 + n^6 + n^5 + n^4 + n^3 + n^2 + n^1 + 1.
a(n) = (n^2 + n + 1) * (n^4 + n^3 + n^2 + n + 1) * (n^8 - n^7 + n^5 - n^4 + n^3 - n + 1). - Jonathan Vos Post, Apr 23 2005
G.f.: (x^14 +10908*x^13 +3423487*x^12 +162086420*x^11 +2236727781*x^10 +11806635128*x^9 +27116815299*x^8 +28635678216*x^7 +13957353555*x^6 +2999111468*x^5 +253732221*x^4 +6684068*x^3 +32647*x^2 +1)/(1-x)^15. - Colin Barker, Nov 04 2012
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MATHEMATICA
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With[{f=Total[n^Range[0, 14]]}, Table[f, {n, 0, 20}]] (* Harvey P. Dale, Jun 11 2011 *)
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PROG
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(Sage) [sum(n^j for j in (0..14)) for n in (0..20)] # G. C. Greubel, Apr 15 2019
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CROSSREFS
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Cf. similar sequences of the type a(n) = Sum_{j=0..m} n^j are: A000027 (m=1), A002061 (m=2), A053698 (m=3), A053699 (m=4), A053700 (m=5), A053716 (m=6), A053717 (m=7), A102909 (m=8), A103623 (m=9), A060885 (m=10), A105067 (m=11), A060887 (m=12), A104376 (m=13), this sequence (m=14), A105312 (m=15), A269442 (m=16), A269446 (m=18).
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KEYWORD
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nonn,easy
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AUTHOR
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Douglas Winston (douglas.winston(AT)srupc.com), Apr 22 2005
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EXTENSIONS
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STATUS
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approved
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