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 A171193 #20 Jul 06 2025 10:08:41
%S A171193 1,1,7,109,3207,174581,17929279,3559607005,1389312382199,
%T A171193 1075527698708485,1658535837898129263,5105026337441341642861,
%U A171193 31395991691829167745766311,385982564381552315528268500501
%N A171193 G.f. A(x) satisfies A(x) = 1/(1 - x*A(2*x)^3).
%H A171193 Seiichi Manyama, <a href="/A171193/b171193.txt">Table of n, a(n) for n = 0..80</a>
%F A171193 a(n) ~ c * 2^(n*(n-1)/2) * 3^n, where c = 0.80142677004566734464115933731029720165641... - _Vaclav Kotesovec_, Nov 03 2021
%F A171193 a(0) = 1; a(n) = 2^(n-1) * Sum_{i, j, k, l>=0 and i+j+k+l=n-1} (1/2)^i * a(i) * a(j) * a(k) * a(l). - _Seiichi Manyama_, Jul 06 2025
%t A171193 nmax = 15; A[_] = 0; Do[A[x_] = 1/(1 - x*A[2*x]^3) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] (* _Vaclav Kotesovec_, Nov 03 2021 *)
%o A171193 (PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=1/(1-x*subst(A, x, 2*x)^3) ); polcoeff(A, n)}
%Y A171193 Cf. A015083, A171192, A171194-A171198.
%Y A171193 Cf. A168601.
%K A171193 nonn
%O A171193 0,3
%A A171193 _Paul D. Hanna_, Dec 05 2009