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 A385953 #8 Jul 13 2025 11:01:25
%S A385953 1,1,6,101,3756,271256,34761512,7372486163,2448035959989,
%T A385953 1216747945481685,872431867857009866,875060598719254613963,
%U A385953 1196215918953589596769516,2179513438308809548333358500,5191611931593198935913809439220,15896735560092998091331427433546666
%N A385953 a(0) = 1; a(n) = Sum_{k=0..n-1} binomial(k+4,4) * a(k) * a(n-1-k).
%F A385953 G.f. A(x) satisfies A(x) = 1/( 1 - Sum_{k=0..4} binomial(4,k) * x^(k+1)/k! * (d^k/dx^k A(x)) ), where (d^0/dx^0 A(x)) = A(x) by convention.
%o A385953 (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, i-1, binomial(j+4, 4)*v[j+1]*v[i-j])); v;
%Y A385953 Cf. A088716, A351798, A385952, A385954, A385955.
%Y A385953 Cf. A385946.
%K A385953 nonn
%O A385953 0,3
%A A385953 _Seiichi Manyama_, Jul 13 2025