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 A385920 #13 Aug 04 2025 18:51:23
%S A385920 1,1,3,34,1085,76176,10075567,2259237184,795650626521,415436957516800,
%T A385920 307467426910853051,311183690415601457664,418253671031607891057877,
%U A385920 728624453608629352377831424,1611758187912750506708147828775,4448533739124778044473142239512576
%N A385920 E.g.f. A(x) satisfies A(x) = exp(x*A(x) + x^3*A''(x)).
%F A385920 a(0) = 1; a(n) = Sum_{k=0..n-1} (1 + k^3) * binomial(n-1,k) * a(k) * a(n-1-k).
%t A385920 terms = 16; A[_] = 1; Do[A[x_] = Exp[x*A[x]+x^3*A''[x]] + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] * Range[0,terms-1]! (* _Stefano Spezia_, Aug 04 2025 *)
%o A385920 (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))*binomial(i-1, j)*v[j+1]*v[i-j])); v;
%Y A385920 Cf. A000272, A156326, A385921, A385922, A385923.
%Y A385920 Cf. A385762.
%K A385920 nonn
%O A385920 0,3
%A A385920 _Seiichi Manyama_, Jul 12 2025