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 A386239 #11 Jul 16 2025 10:04:19
%S A386239 1,-1,0,0,1,3,11,47,253,1651,12610,109744,1069355,11520785,135906642,
%T A386239 1741702304,24089599321,357592702647,5669840845462,95623921546478,
%U A386239 1709172658222253,32271612381443479,641820925099092985,13410242452064469153,293676423537521878381
%N A386239 G.f. A(x) satisfies A(x) = 1/( (1+x) * (1 - x^2*A'(x)) ).
%F A386239 a(n) = (-1)^n + (n-1)/2 * Sum_{k=0..n-1} a(k) * a(n-1-k).
%F A386239 a(n) = (-1)^n + Sum_{k=0..n-1} k * a(k) * a(n-1-k).
%t A386239 terms = 25; A[_] = 1; Do[A[x_] = 1/((1+x)(1-x^2*A'[x])) + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* _Stefano Spezia_, Jul 16 2025 *)
%o A386239 (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 A386239 Cf. A143917, A386238.
%K A386239 sign
%O A386239 0,6
%A A386239 _Seiichi Manyama_, Jul 16 2025