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 A386266 #11 Jul 17 2025 09:43:33
%S A386266 1,0,1,5,41,414,5029,71154,1148369,20813552,418536501,9247315593,
%T A386266 222692887441,5805921628194,162930550724369,4897006907712089,
%U A386266 156949282887329569,5343387198219575688,192583054168461798805,7325489802429780722647,293278021624200874980161
%N A386266 G.f. A(x) satisfies A(x) = 1/( (1+x) * (1 - x*A(x) - 2*x^2*A'(x)) ).
%F A386266 a(n) = (-1)^n + n * Sum_{k=0..n-1} a(k) * a(n-1-k).
%F A386266 a(n) = (-1)^n + Sum_{k=0..n-1} (1 + 2*k) * a(k) * a(n-1-k).
%t A386266 terms=21; A[_]=1; Do[A[x_]=1/( (1+x) * (1 - x*A[x] - 2*x^2*A'[x]) )+ O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* _Stefano Spezia_, Jul 17 2025 *)
%o A386266 (PARI) a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=(-1)^i+i*sum(j=0, i-1, v[j+1]*v[i-j])); v;
%Y A386266 Cf. A000699, A376125, A386238.
%K A386266 nonn
%O A386266 0,4
%A A386266 _Seiichi Manyama_, Jul 17 2025