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 A386389 #18 Aug 20 2025 10:56:38
%S A386389 1,9,97,1161,14849,198729,2748641,38977353,563644673,8280210825,
%T A386389 123226850913,1853870946057,28148395838721,430791367720905,
%U A386389 6638484468424929,102918165951351753,1604104541561284097,25121009971212463881,395085505395126968417,6237523016309454855561
%N A386389 Expansion of (1/x) * Series_Reversion( x/(1+9*x+16*x^2) ).
%F A386389 G.f.: 2/(1 - 9*x + sqrt((1-x) * (1-17*x))).
%F A386389 a(n) = (A386387(n+1) - A386387(n))/4.
%F A386389 (n+2)*a(n) = 9*(2*n+1)*a(n-1) - 17*(n-1)*a(n-2) for n > 1.
%F A386389 a(n) = Sum_{k=0..floor(n/2)} 16^k * 9^(n-2*k) * binomial(n,2*k) * Catalan(k).
%F A386389 a(n) = Sum_{k=0..n} 4^k * binomial(n,k) * Catalan(k+1).
%o A386389 (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/(1+9*x+16*x^2))/x)
%Y A386389 Column k=4 of A386408.
%Y A386389 Cf. A002212, A127846, A386362.
%Y A386389 Cf. A000108, A269796, A386387.
%K A386389 nonn
%O A386389 0,2
%A A386389 _Seiichi Manyama_, Aug 20 2025