A052650 E.g.f. 1/((1-2x)(1-x)^2).

1, 4, 22, 156, 1368, 14400, 177840, 2530080, 40844160, 738823680, 14816390400, 326439590400, 7840777190400, 203947385241600, 5711834461132800, 171375956623872000, 5484386299392000000, 186475536553033728000

Offset

0,2

Comments

Related to polynomials derived from 2F1(-n, 1; m+1; -1): see second Maple code below. - John M. Campbell, Aug 27 2012

Links

Alois P. Heinz, Table of n, a(n) for n = 0..150

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 597

Formula

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

Recurrence: {a(0)=1, a(1)=4, (2*n^2+8*n+6)*a(n)+(-3*n-7)*a(n+1)+a(n+2)=0}.

a(n) = (4*2^n-3-n)*n!.

a(n) = n!*A000295(n+2). - R. J. Mathar, Nov 27 2011

Maple

spec := [S, {S=Prod(Sequence(Z), Sequence(Z), Sequence(Union(Z, Z)))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
with(LinearAlgebra); with(PolynomialTools); function1 := proc (m) options operator, arrow; simplify(hypergeom([1, -n], [m+1], -1)*(n+m)!/(m*n!)-2^(n+m)*(m-1)!) end proc; seq(sum(-CoefficientList(function1(s), n)[q], q = 1 .. Dimension(CoefficientVector(function1(s), n))), s = 1 .. 20);
# John M. Campbell, Aug 27, 2012

Mathematica

With[{nn=20}, CoefficientList[Series[1/((1-2x)(1-x)^2), {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, Sep 08 2018 *)

Crossrefs

Sequence in context: A052772 A365124 A371496 * A198053 A197925 A112697

Adjacent sequences: A052647 A052648 A052649 * A052651 A052652 A052653

Keyword

easy,nonn

Author

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

Status

approved