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 A376126 #6 Sep 11 2024 12:22:24
%S A376126 1,2,11,127,2446,69766,2758136,144660949,9742594594,820936644105,
%T A376126 84720182796109,10518406503248799,1547501158599695053,
%U A376126 266325797207877471893,53021169588315247959918,12092601263851930181412631,3132724961425012148414534036,914922971820526793968713748093
%N A376126 a(n) = 1 + Sum_{k=0..n-1} (k+1)^2 * a(k) * a(n-k-1).
%F A376126 G.f. A(x) satisfies: A(x) = 1 / ( (1 - x) * (1 - x * A(x) - 3 * x^2 * A'(x) - x^3 * A''(x)) ).
%t A376126 a[n_] := a[n] = 1 + Sum[(k + 1)^2 a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 17}]
%t A376126 nmax = 17; A[_] = 0; Do[A[x_] = 1/((1 - x) (1 - x A[x] - 3 x^2 A'[x] - x^3 A''[x])) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%Y A376126 Cf. A007317, A321087, A348857, A376095, A376127.
%K A376126 nonn
%O A376126 0,2
%A A376126 _Ilya Gutkovskiy_, Sep 11 2024