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 A376127 #5 Sep 11 2024 12:22:19
%S A376127 1,2,19,565,38056,4886164,1071397370,370880032881,191040201050842,
%T A376127 139853547948358801,140279102716474353325,187136598610376840549341,
%U A376127 323937672908434382002891895,712668454800648677607151322833,1957709831409075714559805601326566,6613164804688226108094777888275765585
%N A376127 a(n) = 1 + Sum_{k=0..n-1} (k+1)^3 * a(k) * a(n-k-1).
%F A376127 G.f. A(x) satisfies: A(x) = 1 / ( (1 - x) * (1 - x * A(x) - 7 * x^2 * A'(x) - 6 * x^3 * A''(x) - x^4 * A'''(x)) ).
%t A376127 a[n_] := a[n] = 1 + Sum[(k + 1)^3 a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 15}]
%t A376127 nmax = 15; A[_] = 0; Do[A[x_] = 1/((1 - x) (1 - x A[x] - 7 x^2 A'[x] - 6 x^3 A''[x] - x^4 A'''[x])) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%Y A376127 Cf. A007317, A321087, A348858, A376096, A376126.
%K A376127 nonn
%O A376127 0,2
%A A376127 _Ilya Gutkovskiy_, Sep 11 2024