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Search: id:A052566
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| A052566 |
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A simple regular expression in a labeled universe. |
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+0
2
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| 2, 1, 4, 6, 48, 120, 1440, 5040, 80640, 362880, 7257600, 39916800, 958003200, 6227020800, 174356582400, 1307674368000, 41845579776000, 355687428096000, 12804747411456000, 121645100408832000
(list; graph; listen)
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OFFSET
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0,1
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LINKS
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INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 508
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FORMULA
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Recurrence: {a(1)=1, a(0)=2, (-2-n^2-3*n)*a(n)+a(n+2)}
Sum(1/2*(1+2*_alpha)*_alpha^(-1-n), _alpha=RootOf(-1+_Z^2))*n!
E.g.f.: (x+2)/(1-x^2).
2n! if n is even, n! if odd.
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MAPLE
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spec := [S, {S=Union(Sequence(Z), Sequence(Prod(Z, Z)))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
a:=n->n!+sum((-1)^k*n!, k=0..n): seq(a(n), n=0..19); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 25 2008
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PROGRAM
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(PARI) a(n)=if(n<0, 0, n!*polcoeff((x+2)/(1-x^2)+x*O(x^n), n))
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CROSSREFS
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Sequence in context: A095012 A019142 A145858 this_sequence A071948 A121722 A059579
Adjacent sequences: A052563 A052564 A052565 this_sequence A052567 A052568 A052569
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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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