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.
%I A001016 M5426 N2357 #85 Jul 07 2025 00:53:10
%S A001016 0,1,256,6561,65536,390625,1679616,5764801,16777216,43046721,
%T A001016 100000000,214358881,429981696,815730721,1475789056,2562890625,
%U A001016 4294967296,6975757441,11019960576,16983563041,25600000000,37822859361,54875873536,78310985281,110075314176
%N A001016 Eighth powers: a(n) = n^8.
%C A001016 Besides the first term, this sequence lists the denominators in Pi^8/9450 = 1 + 1/256 + 1/6561 + 1/65536 + 1/390625 + 1/1679616 + ... - _Mohammad K. Azarian_, Nov 01 2011, edited by _M. F. Hasler_, Jul 03 2025
%C A001016 For n > 0, a(n) is the largest number k such that k + n^4 divides k^2 + n^4. - _Derek Orr_, Oct 01 2014
%C A001016 Fourth powers of squares and squares of 4th powers. Squares composed with themselves twice. - _Wesley Ivan Hurt_, Apr 01 2016
%D A001016 Granino A. Korn and Theresa M. Korn, Mathematical Handbook for Scientists and Engineers, McGraw-Hill Book Company, New York (1968), p. 982.
%D A001016 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A001016 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A001016 T. D. Noe, <a href="/A001016/b001016.txt">Table of n, a(n) for n = 0..1000</a>
%H A001016 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9, -36, 84, -126, 126, -84, 36, -9, 1).
%F A001016 Multiplicative with a(p^e) = p^(8e). - _David W. Wilson_, Aug 01 2001
%F A001016 Totally multiplicative sequence with a(p) = p^8 for primes p. - _Jaroslav Krizek_, Nov 01 2009
%F A001016 G.f.: -x*(1+x)*(x^6+246*x^5+4047*x^4+11572*x^3+4047*x^2+246*x+1)/(x-1)^9. - _R. J. Mathar_, Jan 07 2011
%F A001016 a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) + 40320. - _Ant King_, Sep 24 2013
%F A001016 From _Wesley Ivan Hurt_, Apr 01 2016: (Start)
%F A001016 a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n > 8.
%F A001016 a(n) = A000290(n)^4 = A000290(A000290(A000290(n))).
%F A001016 a(n) = A000583(n)^2. (End)
%F A001016 From _Amiram Eldar_, Oct 08 2020: (Start)
%F A001016 Sum_{n>=1} 1/a(n) = zeta(8) = Pi^8/9450 (A013666).
%F A001016 Sum_{n>=1} (-1)^(n+1)/a(n) = 127*zeta(8)/128 = 127*Pi^8/1209600. (End)
%F A001016 E.g.f.: exp(x)*x*(1 + 127*x + 966*x^2 + 1701*x^3 + 1050*x^4 + 266*x^5 + 28*x^6 + x^7). - _Stefano Spezia_, Jul 29 2022
%p A001016 A001016:=n->n^8: seq(A001016(n), n=0..50); # _Wesley Ivan Hurt_, Apr 01 2016
%t A001016 Table[n^8, {n, 0, 20}] (* _Vladimir Joseph Stephan Orlovsky_, Sep 27 2008 *)
%o A001016 (Maxima) A001016(n):=n^8$
%o A001016 makelist(A001016(n),n,0,30); /* _Martin Ettl_, Nov 05 2012 */
%o A001016 (PARI) A001016(n)=n^8 \\ _Charles R Greathouse IV_, Sep 24 2015
%o A001016 (Magma) [n^8 : n in [0..50]]; // _Wesley Ivan Hurt_, Apr 01 2016
%o A001016 (Python) A001016 = lambda n: n**8 # _M. F. Hasler_, Jul 03 2025
%Y A001016 Cf. A000290 (squares), A000583 (fourth powers), A001014 - A001017 (6th - 9th powers), A008454 (10th powers), A010801 (13th powers).
%Y A001016 Cf. A000542 (partial sums), A022524 (first differences), A013666 (zeta(8)).
%Y A001016 Cf. A003380 - A003390 (sums of 2, ..., 12 eighth powers).
%K A001016 nonn,easy,mult
%O A001016 0,3
%A A001016 _N. J. A. Sloane_
%E A001016 More terms from _James Sellers_, Sep 19 2000