A052878 E.g.f.: log((1-x)/(1-3*x+x^2)).

0, 2, 6, 34, 276, 2928, 38520, 606240, 11118240, 232928640, 5488922880, 143707737600, 4138613740800, 130021152307200, 4425207423436800, 162194949242726400, 6369480464675328000, 266808295408951296000, 11874724735152254976000, 559591803705456377856000

Offset: 0

Author

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

Keywords

• easy
• nonn

Comments

Previous name was: A simple grammar.

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 849

Programs

Maple

spec := [S,{B=Sequence(Z,1 <= card),C=Union(Z,B),S=Cycle(C)},labeled]: seq(combstruct[count](spec,size=n), n=0..20); # end of program
with(combinat):
0, seq( (fibonacci(2*n+1)+fibonacci(2*n-1)-1) * (n-1)!, n=1..20);  # Mark van Hoeij, May 29 2013

PARI

x='x+O('x^66); concat([0],Vec(serlaplace(log(-(-1+x)/(1-3*x+x^2))))) \\ Joerg Arndt, May 29 2013

Formula

Recurrence: {a(1)=2, a(2)=6, a(3)=34, (-n^3-2*n-3*n^2)*a(n)+(4*n^2+12*n+8)*a(n+1)+(-4*n-8)*a(n+2)+a(n+3)}

For n > 0, a(n) = (n-1)! * (phi^(2*n) + 1/phi^(2*n) - 1), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - Vaclav Kotesovec, Jun 06 2019

Extensions

New name using e.g.f., Vaclav Kotesovec, Jun 06 2019