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 A386230 #12 Jul 16 2025 10:04:06
%S A386230 1,4,18,114,945,9399,106645,1342028,18409725,272154510,4300884555,
%T A386230 72225827628,1283066570500,24025524690426,472822444534395,
%U A386230 9755834028122904,210600429263424372,4747647482075588598,111583282733838959542,2729989048854423409090,69430953497076613542366
%N A386230 G.f. A(x) satisfies A(x) = 1/( (1-x)^3 * (1 - x*A(x) - x^2*A'(x)) ).
%F A386230 a(n) = binomial(n+2,2) + (n+1)/2 * Sum_{k=0..n-1} a(k) * a(n-1-k).
%F A386230 a(n) = binomial(n+2,2) + Sum_{k=0..n-1} (1 + k) * a(k) * a(n-1-k).
%t A386230 terms = 21; A[_] = 1; Do[A[x_] = 1/((1-x)^3(1-x*A[x]-x^2*A'[x])) + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* _Stefano Spezia_, Jul 16 2025 *)
%o A386230 (PARI) a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=binomial(i+2, 2)+(i+1)/2*sum(j=0, i-1, v[j+1]*v[i-j])); v;
%Y A386230 Cf. A088716, A321087, A386229.
%Y A386230 Cf. A386212.
%K A386230 nonn
%O A386230 0,2
%A A386230 _Seiichi Manyama_, Jul 16 2025