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 A383281 #16 Apr 24 2025 04:34:28
%S A383281 1,2,11,120,2202,61260,2407770,127116360,8680455000,744631438320,
%T A383281 78393873940200,9938444069030400,1493483322288157200,
%U A383281 262511581007832156000,53360641241377862792400,12420661873849173800856000,3282370875452495120806512000,977378127650967704776130016000
%N A383281 a(n) = Sum_{k=0..n} (2*k+1) * (1/2)^(n+k) * (2*k)! * (n-k)! * binomial(n,k)^2.
%F A383281 a(n) = (n!)^2 * Sum_{k=0..n} (-1)^k * (1/2)^(n-k) * binomial(-3/2,k)/(n-k)!.
%F A383281 a(n) = (n!)^2 * [x^n] 1/(1-x)^(3/2) * exp(x/2).
%F A383281 a(n) = n * ( (n+1)*a(n-1) - (n-1)^2/2 * a(n-2) ) for n > 1.
%F A383281 a(n) = A002018(n+1)/(n+1).
%F A383281 a(n) ~ 4 * sqrt(Pi) * n^(2*n + 3/2) / exp(2*n - 1/2). - _Vaclav Kotesovec_, Apr 24 2025
%o A383281 (PARI) a(n) = sum(k=0, n, (2*k+1)*(2*k)!*(n-k)!*binomial(n, k)^2/2^(n+k));
%Y A383281 Cf. A002018.
%K A383281 nonn
%O A383281 0,2
%A A383281 _Seiichi Manyama_, Apr 22 2025