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.

A001594 a(n) = 6^n + n^6.

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%I A001594 #31 Jan 07 2023 13:17:52
%S A001594 1,7,100,945,5392,23401,93312,397585,1941760,10609137,61466176,
%T A001594 364568617,2179768320,13065520825,78371693632,470196375201,
%U A001594 2821126684672,16926683582305,101559990680640,609359787056377
%N A001594 a(n) = 6^n + n^6.
%H A001594 Vincenzo Librandi, <a href="/A001594/b001594.txt">Table of n, a(n) for n = 0..1000</a>
%H A001594 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (13,-63,161,-245,231,-133,43,-6).
%F A001594 G.f.: (1 - 6*x + 72*x^2 - 75*x^3 - 1475*x^4 - 1776*x^5 - 334*x^6 - 7*x^7)/((1-x)^7*(1-6*x)). - _Vincenzo Librandi_, Aug 28 2014
%p A001594 seq(seq(k^n+n^k, k=6..6), n=0..19); # _Zerinvary Lajos_, Jun 29 2007
%t A001594 Table[6^n + n^6, {n, 0, 30}] (* or *) CoefficientList[Series[(1 - 6 x + 72 x^2 - 75 x^3 - 1475 x^4 - 1776 x^5 - 334 x^6 - 7 x^7)/((1-x)^7 (1-6 x)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Aug 28 2014 *)
%t A001594 LinearRecurrence[{13,-63,161,-245,231,-133,43,-6},{1,7,100,945,5392,23401,93312,397585},20] (* _Harvey P. Dale_, Jan 07 2023 *)
%o A001594 (PARI) a(n)=6^n+n^6 \\ _Charles R Greathouse IV_, Feb 14 2011
%o A001594 (Magma) [6^n+n^6: n in [0..30]]; // _Vincenzo Librandi_, Oct 27 2011
%o A001594 (Sage) [6^n+n^6 for n in (0..30)] # _Bruno Berselli_, Aug 28 2014
%Y A001594 Cf. sequences of the form k^n+n^k: A001580 (k=2), A001585 (k=3), A001589 (k=4), A001593 (k=5), this sequence (k=6), A001596 (k=7), A198401 (k=8), A185277 (k=9), A177068 (k=10), A177069 (k=11).
%K A001594 nonn,easy
%O A001594 0,2
%A A001594 _N. J. A. Sloane_