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 A386511 #9 Jul 24 2025 07:24:38
%S A386511 1,1,3,43,1889,198661,42947941,17142237365,11658352652969,
%T A386511 12696712215226345,21077148910182673081,51239319321668728761281,
%U A386511 176469705716413028667777349,837352955330191136544190873989,5345677943448502627987168885274813,44983970430636919384496638254796550221
%N A386511 a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} (1 + k) * binomial(k+2,3) * binomial(n-1,k) * a(k) * a(n-1-k).
%F A386511 E.g.f. A(x) satisfies A(x) = exp( x + x*Sum_{k=1..3} binomial(2,k-1) * x^k/k! * (d^k/dx^k A(x)) ).
%o A386511 (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=v[i]+sum(j=0, i-1, (1+j)*binomial(j+2, 3)*binomial(i-1, j)*v[j+1]*v[i-j])); v;
%Y A386511 Cf. A143925, A386510, A386512, A386513.
%Y A386511 Cf. A385945, A386453.
%K A386511 nonn
%O A386511 0,3
%A A386511 _Seiichi Manyama_, Jul 24 2025