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 A386265 #9 Jul 17 2025 09:43:06
%S A386265 1,-1,-1,-3,-11,-61,-469,-4711,-58071,-842361,-13995017,-261468651,
%T A386265 -5420285859,-123390215413,-3058937910365,-82014781572431,
%U A386265 -2364353822942639,-72922308541928945,-2395804482405465233,-83528123730918481747,-3079941980238262567995
%N A386265 G.f. A(x) satisfies A(x) = 1/(1+x) + x^2 * (d/dx A(x)^2).
%F A386265 a(n) = (-1)^n + (n-1) * Sum_{k=0..n-1} a(k) * a(n-1-k).
%F A386265 a(n) = (-1)^n + 2 * Sum_{k=0..n-1} k * a(k) * a(n-1-k).
%t A386265 terms=21; A[_]=1; Do[A[x_]=1/(1+x) + 2x^2 * A[x]A'[x] + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* _Stefano Spezia_, Jul 17 2025 *)
%o A386265 (PARI) a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=(-1)^i+(i-1)*sum(j=0, i-1, v[j+1]*v[i-j])); v;
%Y A386265 Cf. A386208, A386239, A386266.
%K A386265 sign
%O A386265 0,4
%A A386265 _Seiichi Manyama_, Jul 17 2025