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 A257386 #20 Apr 09 2017 03:02:35
%S A257386 1,1,2,4,9,21,51,126,316,799,2034,5202,13357,34407,88888,230237,
%T A257386 597829,1555962,4058944,10612102,27807135,73025751,192204957,
%U A257386 507025163,1340545113,3552492126
%N A257386 Number of Motzkin paths of length n with no level steps at height 3.
%H A257386 G. C. Greubel, <a href="/A257386/b257386.txt">Table of n, a(n) for n = 0..1000</a>
%F A257386 a(n) = a(n-1) + Sum_{j=0..n-2} A252354(j)*a(n-j).
%F A257386 G.f: 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 A257386 a(n) ~ 3^(n+3/2)/(50*sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, Apr 24 2015
%t A257386 CoefficientList[Series[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 A257386 (PARI) x='x+O('x^50); Vec(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_, Apr 08 2017
%Y A257386 Cf. A005043, A217312, A252354.
%K A257386 nonn
%O A257386 0,3
%A A257386 _José Luis Ramírez Ramírez_, Apr 21 2015