A052642 Expansion of e.g.f. x^2*(2+x-x^2)/(1-x).

0, 0, 4, 18, 48, 240, 1440, 10080, 80640, 725760, 7257600, 79833600, 958003200, 12454041600, 174356582400, 2615348736000, 41845579776000, 711374856192000, 12804747411456000, 243290200817664000

Offset

0,3

Links

Table of n, a(n) for n=0..19.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 588

Formula

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

Recurrence: {a(1)=0, a(0)=0, (-1-n)*a(n)+a(n+1)=0, a(2)=4, a(4)=48, a(3)=18}

2*n!

a(n) = A052628(n), n>1. - R. J. Mathar, Jan 30 2009

Maple

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

Mathematica

With[{nn=20}, CoefficientList[Series[x^2 (2+x-x^2)/(1-x), {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, Sep 04 2020 *)

Crossrefs

Cf. A052628.

Sequence in context: A181860 A027271 A073991 * A102928 A081528 A056147

Adjacent sequences: A052639 A052640 A052641 * A052643 A052644 A052645

Keyword

easy,nonn

Author

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

Status

approved