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 A386533 #13 Aug 04 2025 18:45:58
%S A386533 1,1,3,19,225,4576,149517,7448134,542269961,55702422400,7832607617351,
%T A386533 1468762340728464,359026336711386577,112153290859090469184,
%U A386533 44001791667365123420025,21354097196759712722857776,12647439446531876144344860113,9033421564454672567830839315456
%N A386533 E.g.f. A(x) satisfies A(x) = exp(x * A(x) + x^3/6 * A''(x)).
%F A386533 a(0) = 1; a(n) = Sum_{k=0..n-1} (1 + k) * (1 + (-k + k^2)/6) * binomial(n-1,k) * a(k) * a(n-1-k).
%t A386533 terms = 18; A[_] = 1; Do[A[x_] = Exp[x*A[x]+ x^3A''[x]/6] + O[x]^terms // Normal, terms]; CoefficientList[A[x], x]Range[0,terms-1]! (* _Stefano Spezia_, Aug 04 2025 *)
%o A386533 (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, i-1, (1+j)*(1+sum(k=1, 2, stirling(2, k, 1)*j^k)/6)*binomial(i-1, j)*v[j+1]*v[i-j])); v;
%Y A386533 Cf. A156325, A385101, A386534.
%Y A386533 Cf. A385920.
%K A386533 nonn
%O A386533 0,3
%A A386533 _Seiichi Manyama_, Jul 24 2025