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 A141353 #15 Mar 19 2018 05:41:36
%S A141353 1,3,6,13,30,74,196,557,1686,5374,17820,60834,212108,751092,2690824,
%T A141353 9727613,35423206,129775862,477900844,1767787478,6565168996,
%U A141353 24468364172,91486757944,343068002258,1289920924540,4861979955884
%N A141353 a(n) = Catalan(n) + 2^n - 0^n.
%C A141353 Hankel transform is A141354.
%F A141353 G.f.: c(x)+2x/(1-2x), where c(x) is the g.f. of A000108. [corrected by _Paul Barry_, Oct 18 2010]
%F A141353 Conjecture: (n+1)*a(n) + 2*(-4*n+1)*a(n-1) + 4*(5*n-7)*a(n-2) + 8*(-2*n+5)*a(n-3) = 0. - _R. J. Mathar_, Nov 15 2012
%t A141353 f[n_] := Binomial[2n, n]/(n + 1) + 2^n - 0^n; f[0] = 1; Array[f, 29, 0] (* or *)
%t A141353 CoefficientList[ Series[1 + 1/2 (-4 + 2/(1 - 2x) + (1 - Sqrt[1 - 4x])/x), {x, 0, 28}], x] (* _Robert G. Wilson v_, Mar 18 2018 *)
%o A141353 (PARI) a(n) = binomial(2*n,n)/(n+1) + 2^n - 0^n; \\ _Michel Marcus_, Mar 18 2018
%Y A141353 Cf. A000108 (Catalan numbers), A141351.
%K A141353 easy,nonn
%O A141353 0,2
%A A141353 _Paul Barry_, Jun 27 2008