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 A352006 #6 Mar 01 2022 07:28:39
%S A352006 1,1,1,3,5,11,21,59,117,283,597,1467,3125,7387,16149,39931,87541,
%T A352006 207643,463061,1107515,2473909,5819739,13132437,31080571,70236533,
%U A352006 164315035,373572693,875121339,1991869237,4639482331,10599986709,24765957371,56617082101
%N A352006 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} 2^k * a(k) * a(n-2*k-1).
%F A352006 G.f. A(x) satisfies: A(x) = 1 / (1 - x * A(2*x^2)).
%t A352006 a[0] = 1; a[n_] := a[n] = Sum[2^k a[k] a[n - 2 k - 1], {k, 0, Floor[(n - 1)/2]}]; Table[a[n], {n, 0, 32}]
%t A352006 nmax = 32; A[_] = 0; Do[A[x_] = 1/(1 - x A[2 x^2]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%Y A352006 Cf. A000621, A015083, A352007, A352008.
%K A352006 nonn
%O A352006 0,4
%A A352006 _Ilya Gutkovskiy_, Feb 28 2022