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 A386531 #10 Jul 25 2025 02:17:18
%S A386531 1,1,1,2,13,181,4551,188021,11924753,1103029649,142906232381,
%T A386531 25095114042461,5813156139567261,1736262706526700925,
%U A386531 655797361805578202939,308047913827328021014851,177358895717746915172030241,123578165227603044619210348321
%N A386531 E.g.f. A(x) satisfies A(x) = exp(x + x^3/6 * A''(x)).
%F A386531 a(0) = 1; a(n) = a(n-1) + (1/6) * Sum_{k=0..n-1} (-k + k^3) * binomial(n-1,k) * a(k) * a(n-1-k).
%o A386531 (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=v[i]+sum(j=0, i-1, (1+j)*sum(k=1, 2, stirling(2, k, 1)*j^k)*binomial(i-1, j)*v[j+1]*v[i-j])/6); v;
%Y A386531 Cf. A385322, A386532.
%Y A386531 Cf. A362381, A385066.
%K A386531 nonn
%O A386531 0,4
%A A386531 _Seiichi Manyama_, Jul 24 2025