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 A386238 #10 Jul 16 2025 10:04:14
%S A386238 1,0,1,3,16,98,708,5827,53758,548879,6142379,74756975,983186673,
%T A386238 13897204929,210128473576,3384688592135,57868599692392,
%U A386238 1046744442623159,19972732558110246,400941834927714249,8447457715944191407,186387757159393453454,4298157267300757437962
%N A386238 G.f. A(x) satisfies A(x) = 1/( (1+x) * (1 - x*A(x) - x^2*A'(x)) ).
%F A386238 a(n) = (-1)^n + (n+1)/2 * Sum_{k=0..n-1} a(k) * a(n-1-k).
%F A386238 a(n) = (-1)^n + Sum_{k=0..n-1} (1 + k) * a(k) * a(n-1-k).
%t A386238 terms = 23; A[_] = 1; Do[A[x_] = 1/((1+x)(1-x*A[x]-x^2*A'[x])) + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* _Stefano Spezia_, Jul 16 2025 *)
%o A386238 (PARI) a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=(-1)^i+(i+1)/2*sum(j=0, i-1, v[j+1]*v[i-j])); v;
%Y A386238 Cf. A321087, A386239.
%K A386238 nonn
%O A386238 0,4
%A A386238 _Seiichi Manyama_, Jul 16 2025