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 A386965 #6 Aug 12 2025 06:47:28
%S A386965 1,10,294,16296,1458120,191751120,34807535280,8337722440320,
%T A386965 2547572372311680,966944845408147200,446304490431888211200,
%U A386965 246166572372916851532800,159902551429370021259187200,120818209587660157360960972800,105060730670227917425027835648000
%N A386965 Number of permutations p of [2*n] such that there is at least one index i in [2*n-1] with p(i+1) = n + p(i).
%C A386965 Problem 6 at IMO '89 essentially asks to show that a(n) > (2*n)!/4.
%H A386965 30th International Mathematical Olympiad (1989), <a href="https://www.imo-official.org/problems.aspx">Problem 6</a>.
%H A386965 <a href="/index/O#Olympiads">Index to sequences related to Olympiads</a>.
%F A386965 a(n) = Sum_{k=1..n} (-1)^(k+1) * binomial(n,k) * (2*n - k)!.
%F A386965 a(n) = (2*n)! * (1 - 1F1(-n; -2*n; -1)).
%F A386965 a(n) = n! * A324361(n).
%e A386965 The 10 permutations corresponding to a(2) are 1243, 1324, 1342, 2134, 2413, 2431, 3124, 3241, 4132, 4213.
%t A386965 a[n_] := Sum[(-1)^(k+1) Binomial[n, k] (2 n - k)!, {k, n}]; Array[a, 15]
%Y A386965 Cf. A002674, A324361, A159960.
%K A386965 nonn,easy
%O A386965 1,2
%A A386965 _Giovanni Resta_, Aug 11 2025