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 A385922 #13 Aug 04 2025 18:47:51
%S A385922 1,1,3,16,125,16296,11929927,30230776864,203634850471929,
%T A385922 3082625458810336000,93280255561776693446891,
%U A385922 5173509703646410927969711104,491814532626655136406839912703157,75968624000349445912469318939348786176,18252829396078618393615717880609268502659375
%N A385922 E.g.f. A(x) satisfies A(x) = exp(x*A(x) + x^5*A''''(x)).
%F A385922 a(0) = 1; a(n) = Sum_{k=0..n-1} (1 + k) * (1 - 6*k + 11*k^2 - 6*k^3 + k^4) * binomial(n-1,k) * a(k) * a(n-1-k).
%t A385922 terms = 15; A[_] = 1; Do[A[x_] = Exp[x*A[x]+x^5*A''''[x]] + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] * Range[0,terms-1]! (* _Stefano Spezia_, Aug 04 2025 *)
%o A385922 (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, 4, stirling(4, k, 1)*j^k))*binomial(i-1, j)*v[j+1]*v[i-j])); v;
%Y A385922 Cf. A000272, A156326, A385920, A385921, A385923.
%Y A385922 Cf. A385764.
%K A385922 nonn
%O A385922 0,3
%A A385922 _Seiichi Manyama_, Jul 12 2025