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 A385830 #14 Jul 12 2025 21:33:39
%S A385830 1,1,3,20,241,4623,130300,5100750,265780029,17827454651,1498498011875,
%T A385830 154408489507578,19151761451917580,2815820822235814540,
%U A385830 484383420815495253624,96401320782466194458886,21981036279413999807199045,5693391431445001330242504699,1662538953499888924638316487305
%N A385830 a(0) = 1; a(n) = Sum_{k=0..n-1} (1 + k^2) * a(k) * a(n-1-k).
%H A385830 Seiichi Manyama, <a href="/A385830/b385830.txt">Table of n, a(n) for n = 0..253</a>
%F A385830 G.f. A(x) satisfies A(x) = 1/( 1 - x*A(x) - x^2 * (d/dx A(x)) - x^3 * (d^2/dx^2 A(x)) ).
%o A385830 (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, i-1, (1+j^2)*v[j+1]*v[i-j])); v;
%Y A385830 Cf. A088716, A385831, A385832, A385833, A385834.
%Y A385830 Cf. A385762, A385835.
%K A385830 nonn
%O A385830 0,3
%A A385830 _Seiichi Manyama_, Jul 09 2025