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 A386263 #12 Jul 17 2025 09:43:23
%S A386263 1,3,15,121,1333,18091,286867,5158385,103226313,2269474723,
%T A386263 54307112951,1404350909545,39020894189245,1159475912653163,
%U A386263 36695329075865083,1232560854783934561,43801551907551784721,1642199848241650875907,64789265823476378293855
%N A386263 G.f. A(x) satisfies A(x) = 1/( (1-x)^2 * (1 - x*A(x) - 2*x^2*A'(x)) ).
%F A386263 a(n) = n + 1 + n * Sum_{k=0..n-1} a(k) * a(n-1-k).
%F A386263 a(n) = n + 1 + Sum_{k=0..n-1} (1 + 2*k) * a(k) * a(n-1-k).
%t A386263 terms=19; A[_]=1; Do[A[x_]=1/( (1-x)^2 * (1 - x*A[x] - 2*x^2*A'[x]) ) + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* _Stefano Spezia_, Jul 17 2025 *)
%o A386263 (PARI) a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=i+1+i*sum(j=0, i-1, v[j+1]*v[i-j])); v;
%Y A386263 Cf. A376125, A386264.
%Y A386263 Cf. A386209, A386229.
%K A386263 nonn
%O A386263 0,2
%A A386263 _Seiichi Manyama_, Jul 17 2025