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A052687
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Expansion of e.g.f. (1+x-x^3)/((1-x)*(1-x^2)).
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1
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1, 2, 6, 18, 96, 480, 3600, 25200, 241920, 2177280, 25401600, 279417600, 3832012800, 49816166400, 784604620800, 11769069312000, 209227898880000, 3556874280960000, 70426110763008000, 1338096104497152000
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OFFSET
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0,2
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LINKS
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FORMULA
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E.g.f.: (1 + x - x^3)/((1-x)*(1-x^2)).
Recurrence: a(0)=1, a(1)=2, a(2)=6, a(3)=18, (n+4)*a(n+2) = (n+2)*a(n+1) + (n+1)*(n+2)*(n+5)*a(n).
a(n) = n! * (2*n + 7 + (-1)^n)/4.
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MAPLE
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spec := [S, {S=Prod(Sequence(Z), Union(Z, Sequence(Prod(Z, Z))))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
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MATHEMATICA
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Table[n!*(2*n+7+(-1)^n)/4 -Boole[n==0], {n, 0, 30}] (* G. C. Greubel, Jun 03 2022 *)
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PROG
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(Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!(Laplace( (1+x-x^3)/((1-x)*(1-x^2)) ))); // G. C. Greubel, Jun 03 2022
(SageMath) [factorial(n)*(n + 3 + ((n+1)%2))/2 - bool(n==0) for n in (0..30)] # G. C. Greubel, Jun 03 2022
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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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