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A052689
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Expansion of e.g.f. (1+x-x^2)/((1-x)*(1-x^2)).
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1
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1, 2, 4, 18, 72, 480, 2880, 25200, 201600, 2177280, 21772800, 279417600, 3353011200, 49816166400, 697426329600, 11769069312000, 188305108992000, 3556874280960000, 64023737057280000, 1338096104497152000, 26761922089943040000, 613091306060513280000
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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^2)/((1-x)*(1-x^2)).
Recurrence: a(0)=1, a(1)=2, a(2)=4, (n+1)*a(n) = n*a(n-1) + (n-1)*n*(n+2)*a(n-2).
a(n) = n!*(2*n + 5 - (-1)^n)/4.
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MAPLE
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spec := [S, {S=Prod(Union(Z, Sequence(Z)), Sequence(Prod(Z, 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[(1+x-x^2)/((1-x)(1-x^2)), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Feb 10 2014 *)
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PROG
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(Magma) [Factorial(n)*(2*n+5-(-1)^n)/4: n in [0..30]]; // G. C. Greubel, Jun 02 2022
(SageMath) [factorial(n)*(n+2 + n%2)/2 for n in (0..40)] # G. C. Greubel, Jun 02 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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