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 A119685 #7 Apr 10 2022 09:46:54
%S A119685 1,1,2,4,8,17,38,88,208,497,1194,2877,6948,16821,40846,99539,243536,
%T A119685 598353,1476370,3657883,9098420,22713077,56887062,142897576,359879600,
%U A119685 908373713,2297266554,5819357841,14762051140,37491373173,95311970590
%N A119685 G.f. satisfies: A(x) = x + A(x^2/(1-x)^2).
%F A119685 a(1) = 1; a(n) = Sum_{k=1..floor(n/2)} binomial(n-1,2*k-1) * a(k). - _Ilya Gutkovskiy_, Apr 07 2022
%e A119685 A(x) = x + x^2 + 2*x^3 + 4*x^4 + 8*x^5 + 17*x^6 + 38*x^7 + 88*x^8 +...
%o A119685 (PARI) {a(n)=local(F=x^2/(1-x+x*O(x^n))^2,A=x);if(n<1,0, for(i=1,#binary(n),A=x+subst(A, x,F));polcoeff(A, n))}
%Y A119685 Cf. A119262.
%K A119685 nonn
%O A119685 1,3
%A A119685 _Paul D. Hanna_, Jun 08 2006