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 A385874 #15 Jul 12 2025 21:33:28
%S A385874 1,1,2,8,57,639,10357,229588,6686619,248013315,11425386222,
%T A385874 640413284553,42933889931191,3393203732253145,312268381507616935,
%U A385874 33107736233111305459,4006699123399932333697,548987463226205098599755,84552444466155546810368421,14544161652321384236939516147
%N A385874 a(n) = 1 + Sum_{k=0..n-1} binomial(k+1,2) * a(k) * a(n-1-k).
%H A385874 Seiichi Manyama, <a href="/A385874/b385874.txt">Table of n, a(n) for n = 0..270</a>
%F A385874 G.f. A(x) satisfies A(x) = 1/( (1 - x) * ( 1 - x^2 * (d/dx A(x)) - x^3/2 * (d^2/dx^2 A(x)) ) ).
%o A385874 (PARI) a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=1+sum(j=0, i-1, binomial(j+1, 2)*v[j+1]*v[i-j])); v;
%Y A385874 Cf. A143917, A385875, A385876, A385877.
%Y A385874 Cf. A385830, A385835, A385840.
%K A385874 nonn
%O A385874 0,3
%A A385874 _Seiichi Manyama_, Jul 11 2025