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 A134762 #15 May 28 2024 18:28:24
%S A134762 1,4,16,58,208,754,2770,10294,38608,145858,554266,2116294,8112466,
%T A134762 31201798,120349798,465352558,1803241168,7000818658,27225405898,
%U A134762 106035791398,413539586458,1614773623318,6312296891158,24700292182798,96742811049298,379231819313254
%N A134762 a(n) = 3*A000984(n) - 2.
%C A134762 Second inverse binomial transform of the sequence = A134763, (same as a(n) but with interpolated two's).
%H A134762 G. C. Greubel, <a href="/A134762/b134762.txt">Table of n, a(n) for n = 0..1000</a>
%F A134762 G.f.: 3/sqrt(1-4*x) - 2/(1-x). - _Sergei N. Gladkovskii_, Nov 21 2013
%F A134762 From _G. C. Greubel_, May 28 2024: (Start)
%F A134762 a(n) = 3*(n+1)*A000108(n) - 2.
%F A134762 a(n) = (2*(2*n-1)*a(n-1) + 2*(3*n-2))/n.
%F A134762 E.g.f.: 3*exp(2*x)*BesselI(0, 2*x) - 2*exp(x). (End)
%t A134762 Table[3*Binomial[2*n,n]-2, {n,0,40}] (* _G. C. Greubel_, May 28 2024 *)
%o A134762 (PARI) a(n) = 3*binomial(2*n, n) - 2; \\ _Michel Marcus_, Nov 22 2013
%o A134762 (Magma) [3*(n+1)*Catalan(n)-2: n in [0..40]]; // _G. C. Greubel_, May 28 2024
%o A134762 (SageMath) [3*binomial(2*n,n) -2 for n in range(41)] # _G. C. Greubel_, May 28 2024
%Y A134762 Cf. A000108, A000984, A134758, A134759, A134760, A134761, A134763, A134770, A134771.
%K A134762 nonn
%O A134762 0,2
%A A134762 _Gary W. Adamson_, Nov 09 2007
%E A134762 More terms from _Michel Marcus_, Nov 22 2013