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 A386264 #12 Jul 17 2025 09:43:27
%S A386264 1,4,22,190,2239,32431,546832,10414132,219845677,5079617326,
%T A386264 127292440606,3435881715553,99351006910147,3063829146597493,
%U A386264 100385767850729656,3483114440490487576,127610457725933245753,4923678697863463464970,199592119100636938629838
%N A386264 G.f. A(x) satisfies A(x) = 1/( (1-x)^3 * (1 - x*A(x) - 2*x^2*A'(x)) ).
%F A386264 a(n) = binomial(n+2,2) + n * Sum_{k=0..n-1} a(k) * a(n-1-k).
%F A386264 a(n) = binomial(n+2,2) + Sum_{k=0..n-1} (1 + 2*k) * a(k) * a(n-1-k).
%t A386264 terms=19; A[_]=1; Do[A[x_]=1/( (1-x)^3 * (1 - x*A[x] - 2*x^2*A'[x]) )+ O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* _Stefano Spezia_, Jul 17 2025 *)
%o A386264 (PARI) a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=binomial(i+2, 2)+i*sum(j=0, i-1, v[j+1]*v[i-j])); v;
%Y A386264 Cf. A376125, A386263.
%Y A386264 Cf. A386210, A386230.
%K A386264 nonn
%O A386264 0,2
%A A386264 _Seiichi Manyama_, Jul 17 2025