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%I #32 Sep 04 2023 19:42:57
%S 1,14,16383,2391484,89478485,1525878906,15672832819,113037178808,
%T 628292358729,2859599056870,11111111111111,37974983358324,
%U 116719860413533,328114698808274,854769755812155,2085209001813616,4803839602528529,10523614159962558,22047845151887119
%N a(n) = Sum_{j=0..13} n^j.
%H Vincenzo Librandi, <a href="/A104376/b104376.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_14">Index entries for linear recurrences with constant coefficients</a>, signature (14,-91,364,-1001,2002,-3003,3432,-3003,2002,-1001,364,-91,14,-1).
%F a(n) = 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.
%F G.f.: (5461*x^12 + 1119288*x^11 + 37443654*x^10 + 372458048*x^9 + 1409085783*x^8 + 2263446576*x^7 + 1598944452*x^6 + 484853760*x^5 + 57484467*x^4 + 2163032*x^3 + 16278*x^2 + 1)/(1-x)^14. - _Colin Barker_, Nov 04 2012
%t Table[1+Sum[n^j, {j,1,13}], {n,0,20}] (* _G. C. Greubel_, Apr 14 2019 *)
%t LinearRecurrence[{14,-91,364,-1001,2002,-3003,3432,-3003,2002,-1001,364,-91,14,-1},{1,14,16383,2391484,89478485,1525878906,15672832819,113037178808,628292358729,2859599056870,11111111111111,37974983358324,116719860413533,328114698808274},20] (* _Harvey P. Dale_, Sep 04 2023 *)
%o (Magma) [(&+[n^j: j in [0..13]]): n in [0..20]]; // _Vincenzo Librandi_, May 01 2011
%o (PARI) a(n)=sum(j=0,13, n^j) \\ _Charles R Greathouse IV_, Oct 07 2015
%o (Sage) [sum(n^j for j in (0..13)) for n in (0..20)] # _G. C. Greubel_, Apr 14 2019
%Y 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), this sequence (m=13), A104682 (m=14), A105312 (m=15), A269442 (m=16), A269446 (m=18).
%K nonn,easy
%O 0,2
%A Douglas Winston (douglas.winston(AT)srupc.com), Apr 16 2005
%E Name changed by _G. C. Greubel_, Apr 14 2019
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