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A052581 E.g.f. (1-x)/(1-x-x^4). 1
1, 0, 0, 0, 24, 120, 720, 5040, 80640, 1088640, 14515200, 199584000, 3353011200, 62270208000, 1220496076800, 24845812992000, 543992537088000, 12804747411456000, 320118685286400000, 8393511928209408000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Except for an initial 1, this is the p-INVERT of (1,1,1,1,1,...) for p(S) = (1 - S)(1 - 2 S); see A291000.  - Clark Kimberling, Aug 24 2017

LINKS

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

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 525

FORMULA

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

Recurrence: {a(1)=0, a(0)=1, a(2)=0, a(3)=0, (-n^4-35*n^2-50*n-24-10*n^3)*a(n) +(-n-4)*a(n+3) +a(n+4)=0}

Sum(-1/283*(9+12*_alpha^3+16*_alpha^2-73*_alpha)*_alpha^(-1-n), _alpha=RootOf(-1+_Z^4+_Z))*n!

a(n)= n!*A017898(n). - R. J. Mathar, Nov 27 2011

MAPLE

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

MATHEMATICA

With[{nn=20}, CoefficientList[Series[(1-x)/(1-x-x^4), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Sep 27 2016 *)

CROSSREFS

Sequence in context: A124657 A342856 A293050 * A052605 A195917 A334189

Adjacent sequences:  A052578 A052579 A052580 * A052582 A052583 A052584

KEYWORD

easy,nonn

AUTHOR

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

STATUS

approved

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Last modified May 18 11:30 EDT 2021. Contains 343995 sequences. (Running on oeis4.)