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 A386534 #11 Aug 04 2025 18:45:33
%S A386534 1,1,3,16,125,1421,26833,968626,70638465,10215072856,2782227253373,
%T A386534 1347216023489436,1099522113403916545,1443781044602756539876,
%U A386534 2930977624516859360997387,8889808786962394898290294048,39115513670641030174644662148305,243377943140592361750259305827057888
%N A386534 E.g.f. A(x) satisfies A(x) = exp(x * A(x) + x^5/120 * A''''(x)).
%F A386534 a(0) = 1; a(n) = Sum_{k=0..n-1} (1 + k) * (1 + (-6*k + 11*k^2 - 6*k^3 + k^4)/120) * binomial(n-1,k) * a(k) * a(n-1-k).
%t A386534 terms = 18; A[_] = 1; Do[A[x_] = Exp[x*A[x]+x^5*A''''[x]/120] + O[x]^terms // Normal, terms]; CoefficientList[A[x], x]Range[0,terms-1]! (* _Stefano Spezia_, Aug 04 2025 *)
%o A386534 (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)/120)*binomial(i-1, j)*v[j+1]*v[i-j])); v;
%Y A386534 Cf. A156325, A385101, A386533.
%Y A386534 Cf. A385922.
%K A386534 nonn
%O A386534 0,3
%A A386534 _Seiichi Manyama_, Jul 24 2025