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 A385617 #14 Jul 05 2025 09:16:52
%S A385617 1,2,10,82,1062,22646,846570,58644858,7808479582,2038568219422,
%T A385617 1054007965984050,1084591195956246130,2226674324358059364150,
%U A385617 9131600163886719149539590,74851744440590132840318820090,1226745312860243142951267683147178,40204124737879503807503331117931168974
%N A385617 G.f. A(x) satisfies A(x) = 1/( 1 - x*(A(x) + A(2*x)) ).
%F A385617 a(0) = 1; a(n) = Sum_{k=0..n-1} (2^k+1) * a(k) * a(n-1-k).
%F A385617 a(n) ~ c * 2^(n*(n-1)/2), where c = 30.250837358072598377515060923766952434821313428993180484... - _Vaclav Kotesovec_, Jul 05 2025
%t A385617 terms = 17; A[_] = 1; Do[A[x_] = 1/( 1 - x*(A[x] + A[2*x]) ) + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* _Stefano Spezia_, Jul 05 2025 *)
%o A385617 (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, i-1, (2^j+1)*v[j+1]*v[i-j])); v;
%Y A385617 Cf. A000051, A015083, A047749, A385618, A385622.
%K A385617 nonn
%O A385617 0,2
%A A385617 _Seiichi Manyama_, Jul 05 2025