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 A386209 #17 Jul 16 2025 10:03:41
%S A386209 1,2,7,40,329,3474,44127,650144,10862273,202632498,4172689415,
%T A386209 94010964072,2300682029417,60787775220578,1725027567563263,
%U A386209 52338601112555648,1691028812744005697,57973475215478590626,2102150579452302435655,80389277428829219813864
%N A386209 G.f. A(x) satisfies A(x) = 1/(1-x)^2 + x^2 * (d/dx A(x)^2).
%F A386209 a(n) = n + 1 + (n-1) * Sum_{k=0..n-1} a(k) * a(n-1-k).
%F A386209 a(n) = n + 1 + 2 * Sum_{k=0..n-1} k * a(k) * a(n-1-k).
%o A386209 (PARI) a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=i+1+(i-1)*sum(j=0, i-1, v[j+1]*v[i-j])); v;
%Y A386209 Cf. A386208, A386210.
%Y A386209 Cf. A386211.
%K A386209 nonn
%O A386209 0,2
%A A386209 _Seiichi Manyama_, Jul 15 2025