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 A385622 #13 Jul 05 2025 09:58:49
%S A385622 1,1,3,20,321,13847,1718124,630600310,691143519765,2269026118814651,
%T A385622 22336295204505116859,659523795328845920952570,
%U A385622 58417979762116119140729740620,15523000838307934869469597031994180,12374377440444177691000805646758968904928,29593162781962095695448333383964939013238970030
%N A385622 G.f. A(x) satisfies A(x) = 1/( 1 - x*(A(x) + A(3*x))/2 ).
%F A385622 a(0) = 1; a(n) = (1/2) * Sum_{k=0..n-1} (3^k+1) * a(k) * a(n-1-k).
%t A385622 terms = 16; A[_] = 1; Do[A[x_] = 1/( 1 - x*(A[x] + A[3*x])/2 )+ O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* _Stefano Spezia_, Jul 05 2025 *)
%o A385622 (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, i-1, (3^j+1)*v[j+1]*v[i-j])/2); v;
%Y A385622 Cf. A007051, A385617.
%Y A385622 Cf. A385621.
%K A385622 nonn
%O A385622 0,3
%A A385622 _Seiichi Manyama_, Jul 05 2025