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A052672 Expansion of e.g.f. (1-x)/(1-x-2*x^2+x^3). 1
1, 0, 4, 6, 120, 600, 10080, 95760, 1693440, 23950080, 475372800, 8821612800, 199743667200, 4533271142400, 116906088499200, 3112264995840000, 90679371374592000, 2757644630028288000, 89895729202126848000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..400

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 620

FORMULA

E.g.f.: (1 - x)/(1 - x - 2*x^2 + x^3).

Recurrence: a(0)=1, a(1)=0, a(2)=4, a(n) = n*a(n-1) + 2*n*(n-1)*a(n-2) - n*(n-1)*(n-2)*a(n-3).

a(n) = (n!/7)*Sum_{alpha=RootOf(Z^3 -2*Z^2 -Z +1)} (3 - alpha)*alpha^(-n).

a(n) = n!*A052547(n). - R. J. Mathar, Nov 27 2011

MAPLE

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

MATHEMATICA

With[{nn=20}, CoefficientList[Series[-(-1+x)/(x^3-2x^2-x+1), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Sep 25 2021 *)

PROG

(Magma) I:=[1, 0, 4]; [n le 3 select I[n] else (n-1)*(Self(n-1) +2*(n-2)*Self(n-2) -(n-2)*(n-3)*Self(n-3)): n in [1..31]]; // G. C. Greubel, Jun 13 2022

(SageMath)

def A052672_list(prec):

    P.<x> = PowerSeriesRing(QQ, prec)

    return P( (1-x)/(1-x-2*x^2+x^3) ).egf_to_ogf().list()

A052672_list(30) # G. C. Greubel, Jun 13 2022

CROSSREFS

Cf. A000142, A052547.

Sequence in context: A012934 A013165 A337466 * A137025 A355232 A176493

Adjacent sequences:  A052669 A052670 A052671 * A052673 A052674 A052675

KEYWORD

easy,nonn

AUTHOR

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

STATUS

approved

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Last modified August 7 23:50 EDT 2022. Contains 355995 sequences. (Running on oeis4.)