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.

A016973 a(n) = (6*n + 5)^5.

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%I A016973 #20 Apr 01 2022 09:10:53
%S A016973 3125,161051,1419857,6436343,20511149,52521875,115856201,229345007,
%T A016973 418195493,714924299,1160290625,1804229351,2706784157,3939040643,
%U A016973 5584059449,7737809375,10510100501,14025517307,18424351793,23863536599,30517578125,38579489651,48261724457
%N A016973 a(n) = (6*n + 5)^5.
%H A016973 Vincenzo Librandi, <a href="/A016973/b016973.txt">Table of n, a(n) for n = 0..1000</a>
%H A016973 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F A016973 a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6). - _Harvey P. Dale_, Sep 24 2014
%F A016973 G.f.: (3125 + 142301*x + 500426*x^2 + 270466*x^3 + 16801*x^4 + x^5)/(-1+x)^6. - _Harvey P. Dale_, Aug 13 2021
%F A016973 From _Amiram Eldar_, Apr 01 2022: (Start)
%F A016973 a(n) = A016969(n)^5.
%F A016973 Sum_{n>=0} 1/a(n) = 3751*zeta(5)/7776 - 11*Pi^5/(3888*sqrt(3)). (End)
%t A016973 (6*Range[0,20]+5)^5 (* or *) LinearRecurrence[{6,-15,20,-15,6,-1},{3125,161051,1419857,6436343,20511149,52521875},20] (* _Harvey P. Dale_, Sep 24 2014 *)
%o A016973 (Magma) [(6*n+5)^5: n in [0..30]]; // _Vincenzo Librandi_, May 07 2011
%Y A016973 Cf. A016969, A016970, A016971, A016972.
%Y A016973 Subsequence of A000584.
%K A016973 nonn,easy
%O A016973 0,1
%A A016973 _N. J. A. Sloane_