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 A386508 #10 Jul 24 2025 07:23:36
%S A386508 1,1,3,295,287917,1475577461,27675935977381,1506650312499716245,
%T A386508 202590228421127415254121,59748112811137686928254493705,
%U A386508 35281260624146463343889980853779081,38809774783723742261321649306513968984201,75004702183951627532765950774478944180316824189
%N A386508 a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} (1 + k) * k^5 * binomial(n-1,k) * a(k) * a(n-1-k).
%F A386508 E.g.f. A(x) satisfies A(x) = exp( x + x*Sum_{k=1..5} Stirling2(5,k) * x^k * (d^k/dx^k A(x)) ).
%o A386508 (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)*j^5*binomial(i-1, j)*v[j+1]*v[i-j])); v;
%Y A386508 Cf. A143925, A386505, A386506, A386507, A386509.
%Y A386508 Cf. A385942, A386446.
%K A386508 nonn
%O A386508 0,3
%A A386508 _Seiichi Manyama_, Jul 24 2025