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 A375393 #19 Sep 10 2024 00:22:22
%S A375393 1,3,30,483,10314,268686,8167068,281975715,10863651474,461227101210,
%T A375393 21377716429860,1073816307452430,58106804389870500,
%U A375393 3370330005649001532,208635817503306332088,13731856676157543219747,957698874584753026878306,70562301536089812703526370,5477354759932929856218644820
%N A375393 a(0) = 1; a(n) = Sum_{k=0..n-1} (4*k+3) * a(k) * a(n-k-1).
%F A375393 G.f. A(x) satisfies: A(x) = 1 + 3 * x * A(x)^2 + 4 * x^2 * A'(x) * A(x).
%t A375393 a[0] = 1; a[n_] := a[n] = Sum[(4 k + 3) a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 18}]
%t A375393 nmax = 18; A[_] = 0; Do[A[x_] = 1 + 3 x A[x]^2 + 4 x^2 A'[x] A[x] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%Y A375393 Cf. A000699, A088716, A151403, A215648, A376086, A376087.
%K A375393 nonn
%O A375393 0,2
%A A375393 _Ilya Gutkovskiy_, Sep 09 2024