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 A257387 #15 Jun 03 2017 19:01:35
%S A257387 1,1,2,4,9,21,51,127,323,834,2179,5743,15238,40637,108800,292200,
%T A257387 786703,2122387,5735596,15522682,42064028,114117541,309918698,
%U A257387 842489130,2292332265,6242655886
%N A257387 Number of Motzkin paths of length n with no level steps at height 4.
%H A257387 G. C. Greubel, <a href="/A257387/b257387.txt">Table of n, a(n) for n = 0..1000</a>
%F A257387 a(n) = a(n-1) + Sum_{j=0..n-2} A257386(j)*a(n-j).
%F A257387 G.f: 1/(1-x-x^2*(1/(1-x-x^2*(1/(1-x-x^2*(1/(1-x-x^2*R(x)))))))), where R(x) is the g.f. of Riordan numbers (A005043).
%F A257387 a(n) ~ 3^(n+1/2)/(24*sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, Apr 24 2015
%t A257387 CoefficientList[Series[1/(1-x-x^2*(1/(1-x-x^2*(1/(1-x-x^2*(1/(1-x-x^2*(1+x-Sqrt[1-2*x-3*x^2])/(2*x*(1+x))))))))), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Apr 24 2015 *)
%o A257387 (PARI) x='x+O('x^50); Vec(1/(1-x-x^2*(1/(1-x-x^2*(1/(1-x-x^2*(1/(1-x-x^2*(1+x-sqrt(1-2*x-3*x^2))/(2*x*(1+x)))))))))) \\ _G. C. Greubel_, Jun 03 2017
%Y A257387 Cf. A005043, A217312, A252354, A257386.
%K A257387 nonn
%O A257387 0,3
%A A257387 _José Luis Ramírez Ramírez_, Apr 21 2015