A052840 a(n) = n*A029767(n-1).

0, 0, 2, 9, 56, 450, 4464, 52920, 731520, 11566800, 206035200, 4083488640, 89137843200, 2124970848000, 54929029478400, 1530259226496000, 45705137084006400, 1456873475016960000, 49362677881380864000

Offset: 0

Author

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

Keywords

• easy
• nonn

Comments

Old name was: A simple grammar.

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 807

Programs

Maple

spec := [S,{B=Sequence(Z,1 <= card),C=Cycle(B),S=Prod(Z,C)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
# alternative
A052840 := proc(n)
    log((-1+x)/(-1+2*x))*x ;
    coeftayl(%,x=0,n)*n! ;
end proc:
seq(A052840(n),n=0..20) ; # R. J. Mathar, Jan 20 2025

Mathematica

Flatten[{0, 0, Table[n!*(2^(n-1) - 1)/(n-1), {n, 2, 20}]}] (* Vaclav Kotesovec, Jun 06 2019 *)

Formula

E.g.f.: log((-1+x)/(-1+2*x))*x.

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

For n > 1, a(n) = n! * (2^(n-1) - 1)/(n-1). - Vaclav Kotesovec, Jun 06 2019