A052587 Expansion of e.g.f. x^2*(1-x)/(1-2*x).

0, 0, 2, 6, 48, 480, 5760, 80640, 1290240, 23224320, 464486400, 10218700800, 245248819200, 6376469299200, 178541140377600, 5356234211328000, 171399494762496000, 5827582821924864000, 209792981589295104000

Offset: 0

Author

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

Keywords

• easy
• nonn

Comments

Essentially the same as A051578. - R. J. Mathar, Feb 22 2008

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 532

Crossrefs

Cf. A051578 (essentially the same), A000165 (double factorial), A000142 (factorial), A000079 (powers of 2).

Programs

Maple

spec := [S,{S=Prod(Z,Z,Sequence(Prod(Z,Sequence(Z))))},labeled]: seq(combstruct[count](spec,size=n), n=0..20);

Mathematica

With[{nn=20},CoefficientList[Series[x^2 (1-x)/(1-2x),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Mar 14 2025 *)

PARI

apply( {A052587(n)=n!<<(n-3)+(n==2)}, [0..19]) \\ M. F. Hasler, Nov 10 2024

Formula

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

Recurrence: a(0) = a(1) = 0, a(2) = 2, a(3) = 6, a(n+1) = 2*(n+1)*a(n) for n > 3.

a(n) = 1/8*2^n*n!, n > 2.

a(n) = A051578(n-2) = (2*n)!!/4!! for n > 2. - M. F. Hasler, Nov 10 2024