OFFSET
0,3
LINKS
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 579
FORMULA
E.g.f.: -x^2*(-x+x^2-1)/(-1+x)^2.
Recurrence: {a(0)=0, a(1)=0, a(2)=2, a(3)=18; for n > 3, a(n) = a(n-1)*n^2/(n-1)}. [Simplified by Jon E. Schoenfield, Aug 11 2017]
For n > 2, a(n) = n*n!.
MAPLE
spec := [S, {S=Prod(Z, Z, Sequence(Z), Union(Z, Sequence(Z)))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
restart:printlevel := -1; a := [0]; T := x->LambertW(-x); f := series(((1+T(x)))/(1-T(x)), x, 24); for m from 1 to 19 do a := [op(a), op(2*m, f)*m! ] od; print(a); # Zerinvary Lajos, Mar 28 2009
MATHEMATICA
With[{nn=20}, CoefficientList[Series[x^2 (1+x-x^2)/(1-x)^2, {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Apr 27 2016 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
STATUS
approved