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 A006529 M4717 #40 Aug 25 2025 04:22:36
%S A006529 0,1,10,57,272,885,2226,4725,8912,15417,24970,38401,56640,80717,
%T A006529 111762,151005,199776,259505,331722,418057,520240,640101,779570,
%U A006529 940677,1125552,1336425,1575626,1845585,2148832,2487997,2865810,3285101,3748800,4259937,4821642
%N A006529 a(n) = (25*n^4-120*n^3+209*n^2-108*n)/6.
%D A006529 M. Gardner, New Mathematical Diversions from Scientific American. Simon and Schuster, NY, 1966, p. 246, gives this as the number of ways to color faces of a cube using at most n colors, but the formula is incorrect (it was corrected in the second printing) - see A047780.
%D A006529 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A006529 Harvey P. Dale, <a href="/A006529/b006529.txt">Table of n, a(n) for n = 0..1000</a>
%H A006529 Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
%H A006529 Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992
%H A006529 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A006529 From _Harvey P. Dale_, Oct 30 2011: (Start)
%F A006529 a(n) = 5*a(n-1)- 10*a(n-2)+ 10*a(n-3)-5*a(n-4)+a(n-5).
%F A006529 G.f.: (-77*x^4-17*x^3-5*x^2-x)/(x-1)^5. (End)
%p A006529 A006529:=-z*(1+5*z+17*z**2+77*z**3)/(z-1)**5; [Conjectured by _Simon Plouffe_ in his 1992 dissertation.]
%t A006529 Table[(25n^4-120n^3+209n^2-108n)/6,{n,0,40}] (* or *) LinearRecurrence[ {5,-10,10,-5,1},{0,1,10,57,272},40] (* _Harvey P. Dale_, Oct 30 2011 *)
%K A006529 nonn,easy,changed
%O A006529 0,3
%A A006529 _N. J. A. Sloane_
%E A006529 _Jud McCranie_ noticed this error and gave the correct version of this sequence (A047780).