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A052623
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E.g.f. x(1-x)^2/(1-3x+x^2).
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0
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0, 1, 2, 18, 192, 2520, 39600, 725760, 15200640, 358162560, 9376819200, 270037152000, 8483597337600, 288734500454400, 10582834303641600, 415593298568448000, 17408598098411520000, 774797125808369664000
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OFFSET
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0,3
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LINKS
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FORMULA
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E.g.f.: x*(-1+x)^2/(1-3*x+x^2)
Recurrence: {a(1)=1, a(0)=0, a(2)=2, (n^2+3*n+2)*a(n)+(-6-3*n)*a(n+1)+a(n+2)=0, a(3)=18}
Sum(-1/5*(-3+7*_alpha)*_alpha^(-1-n), _alpha=RootOf(_Z^2-3*_Z+1))*n!
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MAPLE
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spec := [S, {S=Prod(Z, Sequence(Prod(Z, Sequence(Z), Sequence(Z))))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
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MATHEMATICA
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With[{nn=20}, CoefficientList[Series[x (1-x)^2/(1-3x+x^2), {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, May 30 2021 *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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STATUS
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approved
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