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 A003013 #32 Aug 01 2024 03:05:33
%S A003013 1,1,4,15,52,165,486,1351,3592,9225,23050,56331,135180,319501,745486,
%T A003013 1720335,3932176,8912913,20054034,44826643,99614740,220200981,
%U A003013 484442134,1061158935,2315255832,5033164825
%N A003013 E.g.f. 1 + x*exp(x) + x^2*exp(2*x).
%H A003013 Vincenzo Librandi, <a href="/A003013/b003013.txt">Table of n, a(n) for n = 0..1000</a>
%H A003013 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (8,-25,38,-28,8).
%F A003013 From _Ralf Stephan_, Sep 02 2003: (Start)
%F A003013 a(0) = 1, a(n) = (n^2 - n)*2^n/4 + n.
%F A003013 a(n) = A002999(n) - n = A001815(n) + n. (End)
%F A003013 O.g.f.: 1+x*(-1+4*x-8*x^2+6*x^3) / ( (x-1)^2*(2*x-1)^3 ). - _R. J. Mathar_, Mar 22 2011
%F A003013 a(n) = 8*a(n-1) - 25*a(n-2) + 38*a(n-3) - 28*a(n-4) + 8*a(n-5); a(0)=1, a(1)=1, a(2)=4, a(3)=15, a(4)=52, a(5)=165. - _Harvey P. Dale_, Nov 01 2011
%t A003013 With[{nn=30},CoefficientList[Series[1+x Exp[x]+x^2 Exp[2x],{x,0,nn}],x] Range[0,nn]!] (* or *) Join[{1},LinearRecurrence[{8,-25,38,-28,8},{1,4,15,52,165},30]] (* _Harvey P. Dale_, Nov 01 2011 *)
%o A003013 (PARI) a(n)=([0,1,0,0,0; 0,0,1,0,0; 0,0,0,1,0; 0,0,0,0,1; 8,-28,38,-25,8]^n*[1;1;4;15;52])[1,1] \\ _Charles R Greathouse IV_, Jun 23 2020
%Y A003013 Cf. A048482, A001787, A005183.
%Y A003013 Cf. A002999, A001815.
%K A003013 nonn,easy
%O A003013 0,3
%A A003013 _N. J. A. Sloane_