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 A386299 #9 Jul 18 2025 08:30:09
%S A386299 1,2,9,115,3869,349233,88835413,65934937157,145194342935565,
%T A386299 955092851917410169,18817250316042492760133,
%U A386299 1111535058740789497290819885,196930668231818953760620540315069,104661954649505883286587026252584631249,166867787421063078832424708621648215185207669
%N A386299 a(n) = 1 + Sum_{k=0..n-1} 3^k * binomial(n-1,k) * a(k) * a(n-1-k).
%F A386299 E.g.f. A(x) satisfies A'(x) = exp(x) + A(x) * A(3*x).
%o A386299 (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, 3^j*binomial(i-1, j)*v[j+1]*v[i-j])); v;
%Y A386299 Cf. A054687, A386298, A386300.
%Y A386299 Cf. A345105, A348858.
%K A386299 nonn
%O A386299 0,2
%A A386299 _Seiichi Manyama_, Jul 17 2025