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 A052145 #34 Sep 08 2022 08:44:59
%S A052145 1,9,200,8820,653184,73180800,11564467200,2451889440000,
%T A052145 671854030848000,231125690776780800,97537253236899840000,
%U A052145 49549698749529538560000,29829250083328819200000000,20999962511521107738624000000,17094073187896757112117657600000
%N A052145 a(n) = (2n-1)*(2n-1)!/n.
%C A052145 This is the number of permutations of 2n letters having a cycle of length n. - _Marko Riedel_, Apr 21 2015
%D A052145 R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 7.68(d).
%H A052145 Alois P. Heinz, <a href="/A052145/b052145.txt">Table of n, a(n) for n = 1..225</a>
%H A052145 Math Stackexchange, <a href="http://math.stackexchange.com/questions/1241917/">How many permutations</a>
%F A052145 a(n) = 2*m*m!/(m+1) where m=2n-1.
%F A052145 a(n) = A126074(2n,n). - _Alois P. Heinz_, Apr 21 2017
%F A052145 a(n) = A293211(2n,n). - _Alois P. Heinz_, Oct 11 2017
%e A052145 For n=2, there are 9 permutations of [4] = { 1, 2, 3, 4 } which have a cycle of length 2: each of the 4*3/2 = 6 transpositions, plus the 3 different possible products of two transpositions. - _M. F. Hasler_, Apr 21 2015
%t A052145 Table[(2 n - 1) (2 n - 1)! / n, {n, 30}] (* _Vincenzo Librandi_, Apr 22 2015 *)
%o A052145 (PARI) a(n)=(2*n-1)*(2*n-1)!/n \\ _Charles R Greathouse IV_, Apr 21 2015
%o A052145 (Magma) [(2*n-1)*Factorial(2*n-1)/n: n in [1..20]]; // _Vincenzo Librandi_, Apr 22 2015
%Y A052145 Cf. A126074, A293211.
%K A052145 nonn,easy
%O A052145 1,2
%A A052145 _N. J. A. Sloane_, Jan 23 2000