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 A000338 M3877 N1589 #50 Apr 22 2024 07:16:34
%S A000338 5,18,42,75,117,168,228,297,375,462,558,663,777,900,1032,1173,1323,
%T A000338 1482,1650,1827,2013,2208,2412,2625,2847,3078,3318,3567,3825,4092,
%U A000338 4368,4653,4947,5250,5562,5883,6213,6552,6900,7257,7623,7998,8382,8775,9177,9588,10008,10437,10875,11322,11778
%N A000338 Expansion of x^3*(5-2*x)*(1-x^3)/(1-x)^4.
%D A000338 J. Riordan, Discordant permutations, Scripta Math., 20 (1954), 14-23.
%D A000338 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A000338 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A000338 T. D. Noe, <a href="/A000338/b000338.txt">Table of n, a(n) for n = 3..1000</a>
%H A000338 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 A000338 Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992
%H A000338 J. Riordan, <a href="/A000211/a000211.pdf">Discordant permutations</a>, Scripta Math., 20 (1954), 14-23. [Annotated scanned copy]
%H A000338 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A000338 a(n) = 3*A095794(n-2), n>3. - _R. J. Mathar_, May 30 2022
%F A000338 G.f.: (1+x+x^2)*(5-2*x)*x^3/(1-x)^3. - _Simon Plouffe_ in his 1992 dissertation
%F A000338 Sum_{n>=3} 1/a(n) = log(3)/5 + Pi*sqrt(3)/45 = 0.3406424... - _R. J. Mathar_, Apr 22 2024
%F A000338 a(n) = 5*A005448(n-2) -2*A005448(n-3). - _R. J. Mathar_, Apr 22 2024
%p A000338 ff := n->9/2*n^2-15/2*n; seq(ff(n), n=3..60); # Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001, sequence without a(3).
%t A000338 nn = 100; CoefficientList[Series[(5 - 2 x) (1 - x^3)/(1 - x)^4, {x, 0, nn}], x] (* _T. D. Noe_, Jun 19 2012 *)
%t A000338 LinearRecurrence[{3,-3,1},{5,18,42,75},60] (* _Harvey P. Dale_, Sep 20 2016 *)
%K A000338 nonn,easy
%O A000338 3,1
%A A000338 _N. J. A. Sloane_
%E A000338 More terms from Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001