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 A292716 #15 May 06 2019 06:19:30
%S A292716 1,1,6,54,672,10625,203256,4554697,116842496,3373056027,108134200000,
%T A292716 3809118341028,146170521796608,6066719073261639,270692733123460480,
%U A292716 12917478278285156250,656311833287586742272,35364920064570086779227,2014028255250518880457728,120852950097737555898105210
%N A292716 a(n) = [x^n] 1/(1 - n*x - n*x^2/(1 - n*x - n*x^2/(1 - n*x - n*x^2/(1 - n*x - n*x^2/(1 - ...))))), a continued fraction.
%C A292716 Also coefficient of x^n in the expansion of 1/(n+1) * (1 + n*x + n*x^2)^(n+1). - _Seiichi Manyama_, May 06 2019
%H A292716 Alois P. Heinz, <a href="/A292716/b292716.txt">Table of n, a(n) for n = 0..381</a>
%F A292716 a(n) = [x^n] 2/(1 - n*x + sqrt(1 + n*x*((n - 4)*x - 2))).
%F A292716 a(n) = n! * [x^n] exp(n*x)*BesselI(1,2*sqrt(n)*x)/(sqrt(n)*x), for n > 0.
%F A292716 a(n) = A107267(n,n).
%F A292716 a(n) ~ exp(2*sqrt(n) - 2) * n^(n - 3/4) / (2*sqrt(Pi)). - _Vaclav Kotesovec_, May 05 2019
%t A292716 Table[SeriesCoefficient[1/(1 - n x + ContinuedFractionK[-n x^2, 1 - n x, {i, 1, n}]), {x, 0, n}], {n, 0, 19}]
%t A292716 Table[SeriesCoefficient[2/(1 - n x + Sqrt[1 + n x ((n - 4) x - 2)]), {x, 0, n}], {n, 0, 19}]
%t A292716 Table[n! SeriesCoefficient[E^(n x) Hypergeometric0F1Regularized[2, n x^2], {x, 0, n}], {n, 0, 19}]
%t A292716 Flatten[{1, Table[Sum[Binomial[k+1, n-k+1] * Binomial[n, k] * n^k / (k+1), {k, 0, n}], {n, 1, 20}]}] (* _Vaclav Kotesovec_, May 05 2019 *)
%o A292716 (PARI) {a(n) = polcoef((1+n*x+n*x^2)^(n+1)/(n+1), n)} \\ _Seiichi Manyama_, May 06 2019
%Y A292716 Main diagonal of A107267.
%Y A292716 Cf. A001006, A247496.
%K A292716 nonn
%O A292716 0,3
%A A292716 _Ilya Gutkovskiy_, Sep 21 2017