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 A385921 #12 Aug 04 2025 18:48:24
%S A385921 1,1,3,16,509,66216,24639367,21043463344,35690424280569,
%T A385921 108571039785256960,549371080081204026731,4363111116508031602712064,
%U A385921 51938511093491129409954627637,892615592639462586040781503568896,21469194967164193484102627607895188975,703974996795045871424921458192403079479296
%N A385921 E.g.f. A(x) satisfies A(x) = exp(x*A(x) + x^4*A'''(x)).
%F A385921 a(0) = 1; a(n) = Sum_{k=0..n-1} (1 + k) * (1 + 2*k - 3*k^2 + k^3) * binomial(n-1,k) * a(k) * a(n-1-k).
%t A385921 terms = 16; A[_] = 1; Do[A[x_] = Exp[x*A[x]+x^4*A'''[x]] + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] * Range[0,terms-1]! (* _Stefano Spezia_, Aug 04 2025 *)
%o A385921 (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))*binomial(i-1, j)*v[j+1]*v[i-j])); v;
%Y A385921 Cf. A000272, A156326, A385920, A385922, A385923.
%Y A385921 Cf. A385763.
%K A385921 nonn
%O A385921 0,3
%A A385921 _Seiichi Manyama_, Jul 12 2025