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 A386512 #9 Jul 24 2025 07:24:53
%S A386512 1,1,3,52,3325,598906,255199051,226888865575,382997189880593,
%T A386512 1140957869006770561,5659169551911928576531,
%U A386512 44571684957086887771692731,535930324156886354251195391269,9517054240482595566592327616630965,242627830243798770154326313268171970697
%N A386512 a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} (1 + k) * binomial(k+3,4) * binomial(n-1,k) * a(k) * a(n-1-k).
%F A386512 E.g.f. A(x) satisfies A(x) = exp( x + x*Sum_{k=1..4} binomial(3,k-1) * x^k/k! * (d^k/dx^k A(x)) ).
%o A386512 (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+3, 4)*binomial(i-1, j)*v[j+1]*v[i-j])); v;
%Y A386512 Cf. A143925, A386510, A386511, A386513.
%Y A386512 Cf. A385946, A386454.
%K A386512 nonn
%O A386512 0,3
%A A386512 _Seiichi Manyama_, Jul 24 2025