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Search: id:A052657
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| A052657 |
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A simple regular expression in a labeled universe. |
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+0
2
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| 0, 0, 2, 6, 48, 240, 2160, 15120, 161280, 1451520, 18144000, 199584000, 2874009600, 37362124800, 610248038400, 9153720576000, 167382319104000, 2845499424768000, 57621363351552000, 1094805903679488000
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Stirling transform of -(-1)^n*a(n-1)=[0,0,2,-6,48,-240,...] is A052841(n-1)=[0,0,2,6,38,270,...]. - Michael Somos Mar 04 2004
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LINKS
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INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 604
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FORMULA
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Recurrence: {a(1)=0, a(0)=0, a(2)=2, (-4*n^2-5*n-n^3-2)*a(n)+(-2-n)*a(n+1)+a(n+2)*n}
(1/4*(-1)^(-n)+1/2*n-1/4)*n!
E.g.f.: x^2/((1-x)(1-x^2)).
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MAPLE
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spec := [S, {S=Prod(Z, Z, Sequence(Z), Sequence(Prod(Z, Z)))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
a:=n->sum((-1)^k * (n-k+1) * n!, k=2..n) : seq(a(n), n=0..19); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 18 2007
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PROGRAM
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(PARI) a(n)=if(n<0, 0, n!*polcoeff(x^2/(1-x)/(1-x^2)+x*O(x^n), n))
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CROSSREFS
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Sequence in context: A098710 A052614 A052688 this_sequence A092143 A052593 A052586
Adjacent sequences: A052654 A052655 A052656 this_sequence A052658 A052659 A052660
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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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