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A052688
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E.g.f. x/((1-x)(1-x^3)).
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0
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0, 1, 2, 6, 48, 240, 1440, 15120, 120960, 1088640, 14515200, 159667200, 1916006400, 31135104000, 435891456000, 6538371840000, 125536739328000, 2134124568576000, 38414242234368000, 851515702861824000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 636
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FORMULA
| E.g.f.: x/(-1+x^3)/(-1+x)
Recurrence: {a(1)=1, a(0)=0, a(2)=2, (-39*n-29*n^2-9*n^3-n^4-18)*a(n)+(-n^2-5*n-6)*a(n+1)+(-n-3)*a(n+2)+(n+2)*a(n+3)=0}
(1/3*n+1/3+Sum(-1/9*(1+2*_alpha)*_alpha^(-1-n), _alpha=RootOf(_Z^2+_Z+1)))*n!.
a(n) = n!*A002264(n+2). - R. J. Mathar, Nov 27 2011
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MAPLE
| spec := [S, {S=Prod(Z, Sequence(Z), Sequence(Prod(Z, Z, Z)))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
restart: G(x):=x/(1-x)/(1-x^3): f[0]:=G(x): for n from 1 to 19 do f[n]:=diff(f[n-1], x) od: x:=0: seq(f[n], n=0..19); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 03 2009]
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CROSSREFS
| Sequence in context: A052596 A098710 A052614 * A052657 A092143 A052593
Adjacent sequences: A052685 A052686 A052687 * A052689 A052690 A052691
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KEYWORD
| easy,nonn
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AUTHOR
| encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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