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 A171192 #15 Jul 25 2023 08:17:10
%S A171192 1,1,5,53,1045,37941,2596693,343615093,89402126741,46139256172725,
%T A171192 47433024462021589,97333484052884523765,399068205440018335950357,
%U A171192 3270764880283567936326235445,53601302478763156422575938811989
%N A171192 G.f. satisfies A(x) = 1/(1 - x*A(2x)^2).
%H A171192 Seiichi Manyama, <a href="/A171192/b171192.txt">Table of n, a(n) for n = 0..81</a>
%F A171192 a(0) = 1; a(n) = Sum_{i=0..n-1} Sum_{j=0..n-i-1} 2^(i+j) * a(i) * a(j) * a(n-i-j-1). - _Ilya Gutkovskiy_, Nov 03 2021
%F A171192 a(n) ~ c * 2^(n*(n+1)/2), where c = 1.3216968146657309382653061124105846042506... - _Vaclav Kotesovec_, Nov 03 2021
%t A171192 nmax = 15; A[_] = 0; Do[A[x_] = 1/(1 - x*A[2*x]^2) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] (* _Vaclav Kotesovec_, Nov 03 2021 *)
%o A171192 (PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=1/(1-x*subst(A, x, 2*x)^2) ); polcoeff(A, n)}
%Y A171192 Cf. A015083, A171193-A171198.
%K A171192 nonn
%O A171192 0,3
%A A171192 _Paul D. Hanna_, Dec 05 2009