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 A386300 #10 Jul 18 2025 08:30:05
%S A386300 1,2,1,-5,1,89,1,-2603,1,133265,1,-10449779,1,1161734969,1,
%T A386300 -173838018059,1,33692909616161,1,-8210919096355811,1,
%U A386300 2457354686029706057,1,-886023132463389334523,1,378811390242562021309361,1,-189490246977278296495043411,1,109640147405400620012620910681
%N A386300 a(n) = 1 + Sum_{k=0..n-1} (-1)^k * binomial(n-1,k) * a(k) * a(n-1-k).
%F A386300 E.g.f. A(x) satisfies A'(x) = exp(x) + A(x) * A(-x).
%F A386300 a(2*n) = 1 for n >= 0.
%o A386300 (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=1+sum(j=0, i-1, (-1)^j*binomial(i-1, j)*v[j+1]*v[i-j])); v;
%Y A386300 Cf. A054687, A386298, A386299.
%Y A386300 Cf. A309473, A386301.
%K A386300 sign
%O A386300 0,2
%A A386300 _Seiichi Manyama_, Jul 17 2025