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A052651 E.g.f. (1-x)/(1-x-x^3-x^4+x^5). 1
1, 0, 0, 6, 48, 120, 1440, 25200, 282240, 2903040, 50803200, 958003200, 16286054400, 305124019200, 6887085004800, 160843947264000, 3807947759616000, 98169730154496000, 2746618319757312000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 598

FORMULA

E.g.f.: (1-x)/(1-x-x^4+x^5-x^3)

Recurrence: {a(1)=0, a(0)=1, a(2)=0, a(3)=6, a(4)=48, (n^5+15*n^4+274*n+120+85*n^3+225*n^2)*a(n)+(-14*n^3-71*n^2-154*n-120-n^4)*a(n+1)+(-12*n^2-47*n-60-n^3)*a(n+2)+(-5-n)*a(n+4)+a(n+5)=0}

Sum(1/8519*(138+2003*_alpha-346*_alpha^2-444*_alpha^3+11*_alpha^4)*_alpha^(-1-n), _alpha=RootOf(1-_Z-_Z^4+_Z^5-_Z^3))*n!

a(n)= n!*A052532(n). - R. J. Mathar, Nov 27 2011

MAPLE

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

MATHEMATICA

With[{nn=20}, CoefficientList[Series[(1-x)/(1-x-x^3-x^4+x^5), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Apr 27 2014 *)

CROSSREFS

Sequence in context: A078237 A274131 A259121 * A153796 A250226 A250274

Adjacent sequences:  A052648 A052649 A052650 * A052652 A052653 A052654

KEYWORD

easy,nonn

AUTHOR

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

STATUS

approved

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Last modified February 23 16:27 EST 2020. Contains 332177 sequences. (Running on oeis4.)