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 A000810 #37 Mar 19 2020 16:33:45
%S A000810 1,1,8,26,352,1936,38528,297296,7869952,78098176,2583554048,
%T A000810 31336418816,1243925143552,17831101321216,825787662368768,
%U A000810 13658417358350336,722906928498737152,13551022195053101056
%N A000810 Expansion of e.g.f. (sin x + cos x)/cos 3x.
%H A000810 R. J. Mathar, <a href="/A000810/b000810.txt">Table of n, a(n) for n = 0..200</a>
%F A000810 a(2n) = A000436(n).
%F A000810 (-1)^n*a(2n+1)=1-sum_{i=0,1,...,n-1} (-1)^i*binomial(2n+1,2i+1)*3^(2n-2i)*a(2i+1). - _R. J. Mathar_, Nov 19 2006
%F A000810 a(n) = | 3^n*2^(n+1)*lerchphi(-1,-n,1/3) |. - _Peter Luschny_, Apr 27 2013
%F A000810 a(n) ~ n!*2^(n+1)*3^(n+1/2)/Pi^(n+1) if n is even and a(n) ~ n!*2^(n+1)*3^n/Pi^(n+1) if n is odd. - _Vaclav Kotesovec_, Jun 25 2013
%F A000810 a(n) = (-1)^floor(n/2)*3^n*skp(n, 1/3), where skp(n,x) are the Swiss-Knife polynomials A153641. - _Peter Luschny_, Apr 19 2014
%t A000810 CoefficientList[Series[(Sin[x]+Cos[x])/Cos[3*x], {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Jun 25 2013 *)
%t A000810 Table[Abs[EulerE[n, 1/3]] 6^n, {n, 0, 20}] (* _Vladimir Reshetnikov_, Oct 21 2015 *)
%o A000810 (Sage)
%o A000810 from mpmath import mp, lerchphi
%o A000810 mp.dps = 32; mp.pretty = True
%o A000810 def A000810(n): return abs(3^n*2^(n+1)*lerchphi(-1,-n,1/3))
%o A000810 [int(A000810(n)) for n in (0..17)] # _Peter Luschny_, Apr 27 2013
%o A000810 (PARI) x='x+O('x^66); v=Vec(serlaplace( (sin(x)+cos(x)) / cos(3*x) ) ) \\ _Joerg Arndt_, Apr 27 2013
%Y A000810 Cf. A007286, A007289.
%Y A000810 (-1)^(n*(n-1)/2)*a(n) gives the alternating row sums of A225118. - _Wolfdieter Lang_, Jul 12 2017
%K A000810 nonn
%O A000810 0,3
%A A000810 _N. J. A. Sloane_