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 A302286 #6 Jun 08 2019 11:56:49
%S A302286 1,2,12,116,1530,25422,507696,11814728,313426350,9324499610,
%T A302286 307171539576,11091813369276,435408606414964,18453269887229478,
%U A302286 839464708754178240,40786587211854543120,2107367668847505288726,115352793604678609311282,6667002839420189781109800,405656528458830256952396420
%N A302286 a(n) = [x^n] 1/(1 - n*x - x/(1 - n*x - x/(1 - n*x - x/(1 - n*x - x/(1 - ...))))), a continued fraction.
%F A302286 a(n) = [x^n] (1 - n*x - sqrt(1 - (2*n + 4)*x + n^2*x^2))/(2*x).
%F A302286 a(0) = 1; a(n) = (1/n)*Sum_{k=0..n} (n + 1)^k*binomial(n,k)*binomial(n,k-1).
%F A302286 a(n) = A247507(n,n).
%F A302286 a(n) ~ exp(2*sqrt(n)) * n^(n - 3/4) / (2*sqrt(Pi)). - _Vaclav Kotesovec_, Jun 08 2019
%t A302286 Table[SeriesCoefficient[1/(1 - n x + ContinuedFractionK[-x, 1 - n x, {k, 1, n}]), {x, 0, n}], {n, 0, 19}]
%t A302286 Table[SeriesCoefficient[(1 - n x - Sqrt[1 - (2 n + 4) x + n^2 x^2])/(2 x), {x, 0, n}], {n, 0, 19}]
%t A302286 Join[{1}, Table[(1/n) Sum[(n + 1)^k Binomial[n, k] Binomial[n, k - 1], {k, 0, n}], {n, 1, 19}]]
%t A302286 Table[(n + 1) Hypergeometric2F1[1 - n, -n, 2, n + 1], {n, 0, 19}]
%Y A302286 Main diagonal of A247507.
%Y A302286 Cf. A006318, A099169, A247496, A292798.
%K A302286 nonn
%O A302286 0,2
%A A302286 _Ilya Gutkovskiy_, Apr 04 2018