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 A386432 #27 Aug 22 2025 11:47:22
%S A386432 1,3,29,532,14849,562551,27053749,1581258225,108965790593,
%T A386432 8657148898585,779508506302701,78480330282178738,8738801236865140417,
%U A386432 1066555304017996550265,141604665239501105707269,20321162053065050407161076,3134730687100285268294654465,517309567362171441488395248225
%N A386432 a(n) = Sum_{k=0..n} n^k * binomial(n,k) * Catalan(k+1).
%H A386432 Vincenzo Librandi, <a href="/A386432/b386432.txt">Table of n, a(n) for n = 0..200</a>
%F A386432 a(n) = Sum_{k=0..floor(n/2)} n^(2*k) * (2*n+1)^(n-2*k) * binomial(n,2*k) * Catalan(k).
%t A386432 Table[Sum[(n^k/. 0^0->1)*Binomial[n,k]*CatalanNumber[k+1],{k,0,n}],{n,0,25}] (* _Vincenzo Librandi_, Aug 22 2025 *)
%o A386432 (PARI) a(n) = sum(k=0, n, n^k*binomial(n, k)*(2*(k+1))!/((k+1)!*(k+2)!));
%o A386432 (Magma) [&+[n^k*Binomial(n, k) * Catalan (k+1): k in [0..n]]: n in [0..20]]; // _Vincenzo Librandi_, Aug 22 2025
%Y A386432 Main diagonal of A386408.
%Y A386432 Cf. A000108, A338979.
%K A386432 nonn,changed
%O A386432 0,2
%A A386432 _Seiichi Manyama_, Aug 20 2025