cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A017335 a(n) = (10*n + 5)^7.

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%I A017335 #22 Apr 18 2023 05:02:32
%S A017335 78125,170859375,6103515625,64339296875,373669453125,1522435234375,
%T A017335 4902227890625,13348388671875,32057708828125,69833729609375,
%U A017335 140710042265625,266001988046875,476837158203125,817215093984375,1347646586640625,2149422977421875,3329565857578125
%N A017335 a(n) = (10*n + 5)^7.
%H A017335 Vincenzo Librandi, <a href="/A017335/b017335.txt">Table of n, a(n) for n = 0..10000</a>
%H A017335 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8,-1).
%F A017335 G.f.: 78125*(x+1)*(x^6 + 2178*x^5 + 58479*x^4 + 201244*x^3 + 58479*x^2 + 2178*x + 1)/(x-1)^8. - _Colin Barker_, Nov 13 2012
%F A017335 From _Amiram Eldar_, Apr 18 2023: (Start)
%F A017335 a(n) = A017329(n)^7.
%F A017335 a(n) = 5^7 * A016759(n).
%F A017335 Sum_{n>=0} 1/a(n) = 127*zeta(7)/10000000.
%F A017335 Sum_{n>=0} (-1)^n/a(n) = 61*Pi^7/14400000000. (End)
%t A017335 Table[(10*n + 5)^7, {n, 0, 20}] (* _Amiram Eldar_, Apr 18 2023 *)
%o A017335 (Magma) [(10*n+5)^7: n in [0..25]]; // _Vincenzo Librandi_, Aug 02 2011
%Y A017335 Cf. A013665, A016759, A017329.
%K A017335 nonn,easy
%O A017335 0,1
%A A017335 _N. J. A. Sloane_