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 A386362 #47 Aug 20 2025 10:56:44
%S A386362 1,7,58,532,5209,53347,564499,6123481,67732483,761052565,8662502212,
%T A386362 99671232514,1157409133831,13546774268125,159649564550746,
%U A386362 1892849564159596,22562032457415067,270209749616920813,3249905798884688038,39237866746912398292,475388228365424562019
%N A386362 Expansion of (1/x) * Series_Reversion( x/(1+7*x+9*x^2) ).
%F A386362 G.f.: 2/(1 - 7*x + sqrt((1-x) * (1-13*x))).
%F A386362 a(n) = (A337167(n+1) - A337167(n))/3.
%F A386362 (n+2)*a(n) = 7*(2*n+1)*a(n-1) - 13*(n-1)*a(n-2) for n > 1.
%F A386362 a(n) = Sum_{k=0..floor(n/2)} 9^k * 7^(n-2*k) * binomial(n,2*k) * Catalan(k).
%F A386362 a(n) = Sum_{k=0..n} 3^k * binomial(n,k) * Catalan(k+1).
%o A386362 (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/(1+7*x+9*x^2))/x)
%Y A386362 Column k=3 of A386408.
%Y A386362 Cf. A002212, A127846, A386389.
%Y A386362 Cf. A000108, A337167, A385716.
%K A386362 nonn,new
%O A386362 0,2
%A A386362 _Seiichi Manyama_, Aug 20 2025