|
%I #28 Sep 08 2022 08:45:17
%S 1,15,32767,7174453,357913941,7629394531,94036996915,791260251657,
%T 5026338869833,25736391511831,111111111111111,417724816941565,
%U 1400638324962397,4265491084507563,11966776581370171,31278135027204241,76861433640456465,178901440719363487
%N a(n) = Sum_{j=0..14} n^j.
%H Vincenzo Librandi, <a href="/A104682/b104682.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (15,-105,455,-1365,3003,-5005,6435,-6435,5005,-3003,1365,-455,105,-15,1).
%F 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.
%F 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
%F 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
%t With[{f=Total[n^Range[0,14]]},Table[f,{n,0,20}]] (* _Harvey P. Dale_, Jun 11 2011 *)
%o (Magma) [(&+[n^j: j in [0..14]]): n in [0..20]]; // _Vincenzo Librandi_, May 01 2011
%o (PARI) a(n) = sum(j=0, 14, n^j) \\ _Charles R Greathouse IV_, Oct 07 2015
%o (Sage) [sum(n^j for j in (0..14)) for n in (0..20)] # _G. C. Greubel_, Apr 15 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), A104376 (m=13), this sequence (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 22 2005
%E More terms from _Harvey P. Dale_, Jun 11 2011
%E Name changed by _G. C. Greubel_, Apr 15 2019
|
