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 A052840 #23 Jan 20 2025 06:31:47
%S A052840 0,0,2,9,56,450,4464,52920,731520,11566800,206035200,4083488640,
%T A052840 89137843200,2124970848000,54929029478400,1530259226496000,
%U A052840 45705137084006400,1456873475016960000,49362677881380864000
%N A052840 a(n) = n*A029767(n-1).
%C A052840 Old name was: A simple grammar.
%H A052840 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=807">Encyclopedia of Combinatorial Structures 807</a>
%F A052840 E.g.f.: log((-1+x)/(-1+2*x))*x.
%F A052840 D-finite with recurrence: a(1)=0, a(2)=2, (-2*n+2*n^3-4+4*n^2)*a(n)+(-6*n-3*n^2)*a(n+1)+(n+1)*a(n+2), i.e. (-n+1)*a(n) +3*n*(n-2)*a(n-1) -2*n*(n-1)*(n-3)*a(n-2)=0
%F A052840 For n > 1, a(n) = n! * (2^(n-1) - 1)/(n-1). - _Vaclav Kotesovec_, Jun 06 2019
%p A052840 spec := [S,{B=Sequence(Z,1 <= card),C=Cycle(B),S=Prod(Z,C)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%p A052840 # alternative
%p A052840 A052840 := proc(n)
%p A052840 log((-1+x)/(-1+2*x))*x ;
%p A052840 coeftayl(%,x=0,n)*n! ;
%p A052840 end proc:
%p A052840 seq(A052840(n),n=0..20) ; # _R. J. Mathar_, Jan 20 2025
%t A052840 Flatten[{0, 0, Table[n!*(2^(n-1) - 1)/(n-1), {n, 2, 20}]}] (* _Vaclav Kotesovec_, Jun 06 2019 *)
%K A052840 easy,nonn
%O A052840 0,3
%A A052840 encyclopedia(AT)pommard.inria.fr, Jan 25 2000