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A052641 E.g.f. (1-x)/(1-3x-x^2+x^3). 0
1, 2, 14, 132, 1704, 27360, 527760, 11874240, 305343360, 8833224960, 283928198400, 10038995366400, 387222498432000, 16180539927552000, 728132005791590400, 35106736224688128000, 1805508406018437120000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..16.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 587

FORMULA

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

Recurrence: {a(0)=1, a(1)=2, a(2)=14, (n^3+6*n^2+11*n+6)*a(n)+(-n^2-5*n-6)*a(n+1)+(-3*n-9)*a(n+2)+a(n+3)=0}

Sum(-1/74*(-11-16*_alpha+7*_alpha^2)*_alpha^(-1-n), _alpha=RootOf(1-3*_Z-_Z^2+_Z^3))*n!

a(n) = n!*A030186(n). - R. J. Mathar, Nov 27 2011

MAPLE

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

MATHEMATICA

With[{nn=20}, CoefficientList[Series[(1-x)/(1-3x-x^2+x^3), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Aug 26 2017 *)

CROSSREFS

Sequence in context: A246481 A048990 A089602 * A157085 A073553 A144097

Adjacent sequences:  A052638 A052639 A052640 * A052642 A052643 A052644

KEYWORD

easy,nonn

AUTHOR

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

STATUS

approved

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Last modified October 21 08:27 EDT 2018. Contains 316405 sequences. (Running on oeis4.)