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 A385101 #33 Aug 04 2025 18:51:18
%S A385101 1,1,3,16,141,2161,59842,2979509,258264379,37321303420,8597483041421,
%T A385101 3028595626839564,1572449537786394577,1165432782899826271026,
%U A385101 1199378312656505145280950,1673258190849282722438631406,3099020844849243071430739707913,7481267275389054589164201426886656
%N A385101 E.g.f. A(x) satisfies A(x) = exp(x * A(x) + x^4/24 * A'''(x)).
%F A385101 a(0) = 1; a(n) = Sum_{k=0..n-1} (1 + k) * (1 + (2*k - 3*k^2 + k^3)/24) * binomial(n-1,k) * a(k) * a(n-1-k).
%t A385101 terms = 18; A[_] = 1; Do[A[x_] = Exp[x*A[x]+x^4*A'''[x]/24] + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] * Range[0,terms-1]! (* _Stefano Spezia_, Aug 04 2025 *)
%o A385101 (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, 3, stirling(3, k, 1)*j^k)/24)*binomial(i-1, j)*v[j+1]*v[i-j])); v;
%Y A385101 Cf. A156325, A386533, A386534.
%Y A385101 Cf. A385921.
%K A385101 nonn
%O A385101 0,3
%A A385101 _Seiichi Manyama_, Jul 24 2025