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 A339001 #23 Feb 14 2021 08:13:03
%S A339001 1,0,5,89,2481,93274,4450645,258297570,17689681345,1397903887808,
%T A339001 125286890408901,12562851683433765,1393925069404093105,
%U A339001 169595051215441936902,22454465186157134883285
%N A339001 a(n) = (-1)^n * Sum_{k=0..n} (-n)^k * binomial(n,k) * Catalan(k).
%H A339001 Seiichi Manyama, <a href="/A339001/b339001.txt">Table of n, a(n) for n = 0..322</a>
%F A339001 a(n) = n! * [x^n] exp((2*n-1)*x) * (BesselI(0,2*n*x) - BesselI(1,2*n*x)). - _Ilya Gutkovskiy_, Feb 01 2021
%F A339001 a(n) ~ exp(-1/4) * 4^n * n^(n - 3/2) / sqrt(Pi). - _Vaclav Kotesovec_, Feb 14 2021
%t A339001 a[0] = 1; a[n_] := (-1)^n * Sum[(-n)^k * Binomial[n, k] * CatalanNumber[k], {k, 0, n}]; Array[a, 15, 0] (* _Amiram Eldar_, Feb 01 2021 *)
%o A339001 (PARI) {a(n) = (-1)^n*sum(k=0, n, (-n)^k*binomial(n, k)*(2*k)!/(k!*(k+1)!))}
%Y A339001 Cf. A000108, A005043, A337168, A337169, A338979.
%K A339001 nonn
%O A339001 0,3
%A A339001 _Seiichi Manyama_, Jan 31 2021