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 A082306 #11 Sep 08 2022 08:45:10
%S A082306 1,3,9,29,97,327,1097,3649,12033,39371,127945,413349,1328609,4251535,
%T A082306 13551753,43046729,136314625,430467219,1355971721,4261625389,
%U A082306 13366006881,41841412823,130754415049,407953774929,1270932914177
%N A082306 Expansion of e.g.f. (1+x)*exp(2*x)*cosh(x).
%C A082306 Binomial transform of A082305 a(n)=(A006234(n)+A000027(n))/2
%H A082306 G. C. Greubel, <a href="/A082306/b082306.txt">Table of n, a(n) for n = 0..1000</a>
%H A082306 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (8,-22,24,-9).
%F A082306 a(n) = (n + 1 + 3^(n-1)*(n + 3))/2.
%F A082306 G.f.: (1/(1-x)^2 + (1-2*x)/(1-3*x)^2)/2.
%F A082306 E.g.f.: (1+x)*exp(2*x)*cosh(x).
%t A082306 With[{nmax = 50}, CoefficientList[Series[(1 + x)*Exp[2*x]*Cosh[x], {x, 0, nmax}], x]*Range[0, nmax]!] (* _G. C. Greubel_, Sep 16 2018 *)
%o A082306 (PARI) x='x+O('x^30); Vec(serlaplace((1+x)*exp(2*x)*cosh(x))) \\ _G. C. Greubel_, Sep 16 2018
%o A082306 (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!((1+x)*Exp(2*x)*Cosh(x))); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Sep 16 2018
%Y A082306 Cf. A082307.
%K A082306 easy,nonn
%O A082306 0,2
%A A082306 _Paul Barry_, Apr 09 2003