OFFSET
0,3
LINKS
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 692
FORMULA
D-finite with recurrence: a(1)=0; a(2)=2; a(3)=24; (-n^3-n^2+4*n+4)*a(n) +(-6+7*n^2+11*n)*a(n+1) +(-7*n-10)*a(n+2) +a(n+3) =0.
a(n) ~ (2-sqrt(2))*sqrt(3*sqrt(2)-4)*n^(n-1)*(3+2*sqrt(2))^n/exp(n). - Vaclav Kotesovec, Oct 05 2013
Conjecture: a(n) = n!*A006319(n-1). - R. J. Mathar, Oct 16 2013
MAPLE
spec := [S, {B=Prod(Z, C), S=Prod(C, C), C=Union(B, S, Z)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20); # end of program
0, seq(simplify( n!*(n-1)*hypergeom([n, 2-n], [3], -1) ), n=1..20); # Mark van Hoeij, May 29 2013
MATHEMATICA
CoefficientList[Series[1/2-3/2*x-1/2*(1-6*x+x^2)^(1/2)-(1/2-1/2*x-1/2*(1-6*x+x^2)^(1/2))*x, {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 05 2013 *)
PROG
(PARI) x='x+O('x^66); concat([0, 0], Vec( serlaplace( 1/2-3/2*x -1/2*(1-6*x+x^2)^(1/2) -(1/2-1/2*x-1/2*(1-6*x+x^2)^(1/2))*x))) \\ Joerg Arndt, May 29 2013
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
STATUS
approved