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 A376125 #10 Jul 15 2025 08:22:41
%S A376125 1,2,9,67,681,8556,126253,2124340,39991633,831271006,18893178381,
%T A376125 465972248083,12394713108433,353750057246236,10784915257548041,
%U A376125 349874160411051511,12036066260440602401,437714593034154481686,16780944423208533034861,676482338975579658794689
%N A376125 a(n) = 1 + Sum_{k=0..n-1} (2*k+1) * a(k) * a(n-k-1).
%H A376125 Seiichi Manyama, <a href="/A376125/b376125.txt">Table of n, a(n) for n = 0..402</a>
%F A376125 G.f. A(x) satisfies: A(x) = 1 / ( (1 - x) * (1 - x * A(x) - 2 * x^2 * A'(x)) ).
%F A376125 a(n) ~ c * 2^n * n * n!, where c = 0.6018110636400677977754542011395053310779724922160159... - _Vaclav Kotesovec_, Sep 11 2024
%F A376125 a(n) = 1 + n * Sum_{k=0..n-1} a(k) * a(n-1-k). - _Seiichi Manyama_, Jul 15 2025
%t A376125 a[n_] := a[n] = 1 + Sum[(2 k + 1) a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 19}]
%t A376125 nmax = 19; A[_] = 0; Do[A[x_] = 1/((1 - x) (1 - x A[x] - 2 x^2 A'[x])) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%Y A376125 Cf. A000699, A007317, A321087.
%K A376125 nonn
%O A376125 0,2
%A A376125 _Ilya Gutkovskiy_, Sep 11 2024