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 A338979 #37 Aug 27 2025 06:32:59
%S A338979 1,2,13,199,5073,181776,8413021,478070020,32238960193,2517734880838,
%T A338979 223558608409101,22248413487603887,2453271411779452369,
%U A338979 296925818848604834448,39138393489232585787037,5581250331202285217569351,856182695406472437496803585,140595282922234695782098680030
%N A338979 a(n) = Sum_{k=0..n} n^k * binomial(n,k) * Catalan(k).
%H A338979 Seiichi Manyama, <a href="/A338979/b338979.txt">Table of n, a(n) for n = 0..322</a>
%F A338979 a(n) = n! * [x^n] exp((2*n+1)*x) * (BesselI(0,2*n*x) - BesselI(1,2*n*x)). - _Ilya Gutkovskiy_, Feb 02 2021
%F A338979 a(n) ~ exp(1/4) * 4^n * n^(n - 3/2) / sqrt(Pi). - _Vaclav Kotesovec_, Feb 14 2021
%F A338979 a(n) = hypergeom([1/2, -n], [2], -4*n). - _Peter Luschny_, Aug 27 2025
%p A338979 a := n -> hypergeom([1/2, -n], [2], -4*n):
%p A338979 seq(simplify(a(n)), n = 0..17); # _Peter Luschny_, Aug 27 2025
%t A338979 A338979[n_] := Sum[n^k*Binomial[n, k]*(2*k)!/(k!*(k + 1)!), {k, 0, n}];
%t A338979 Join[{1}, Table[A338979[n], {n, 1, 17}]] (* _Robert P. P. McKone_, Jan 31 2021 *)
%t A338979 A338979[n_] := Hypergeometric2F1[1/2, -n, 2, -4*n]; Table[A338979[n], {n, 0, 17}] (* _Peter Luschny_, Aug 27 2025 *)
%o A338979 (PARI) {a(n) = sum(k=0, n, n^k*binomial(n, k)*(2*k)!/(k!*(k+1)!))}
%Y A338979 Cf. A000108, A007317, A162326, A337167, A339001.
%K A338979 nonn,changed
%O A338979 0,2
%A A338979 _Seiichi Manyama_, Jan 31 2021