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 A385618 #13 Jul 05 2025 09:58:48
%S A385618 1,2,14,230,9014,913334,254986934,203241812630,471322195238102,
%T A385618 3214892041613961206,64937611960188470964662,
%U A385618 3901256965326759127330935830,699101347969640933511109922382422,374397435055450676411068538643233721206,599979003238812649083869782544110463986119734
%N A385618 G.f. A(x) satisfies A(x) = 1/( 1 - x*(A(2*x) + A(3*x)) ).
%F A385618 a(0) = 1; a(n) = Sum_{k=0..n-1} (2^k+3^k) * a(k) * a(n-1-k).
%t A385618 terms = 15; A[_] = 1; Do[A[x_] = 1/( 1 - x*(A[2*x] + A[3*x]) ) + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* _Stefano Spezia_, Jul 05 2025 *)
%o A385618 (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+3^j)*v[j+1]*v[i-j])); v;
%Y A385618 Cf. A007689, A015083, A015084, A047749, A385617.
%K A385618 nonn
%O A385618 0,2
%A A385618 _Seiichi Manyama_, Jul 05 2025