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 A386509 #12 Jul 24 2025 07:23:52
%S A386509 1,1,3,583,1702357,34872788861,3269533221246901,
%T A386509 1067826281292319819285,1005038096045094314876257929,
%U A386509 2371191405228277266497568590592937,12601507027818562471139233302156639660841,138616715922712004054565802733773706346507326441
%N A386509 a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} (1 + k) * k^6 * binomial(n-1,k) * a(k) * a(n-1-k).
%F A386509 E.g.f. A(x) satisfies A(x) = exp( x + x*Sum_{k=1..6} Stirling2(6,k) * x^k * (d^k/dx^k A(x)) ).
%o A386509 (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^6*binomial(i-1, j)*v[j+1]*v[i-j])); v;
%Y A386509 Cf. A143925, A386505, A386506, A386507, A386508.
%Y A386509 Cf. A385943, A386447.
%K A386509 nonn
%O A386509 0,3
%A A386509 _Seiichi Manyama_, Jul 24 2025