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Search: id:A052612
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| A052612 |
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A simple regular expression in a labeled universe. |
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+0
2
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| 0, 2, 2, 12, 24, 240, 720, 10080, 40320, 725760, 3628800, 79833600, 479001600, 12454041600, 87178291200, 2615348736000, 20922789888000, 711374856192000, 6402373705728000, 243290200817664000
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Stirling transform of (-1)^n*a(n-1)=[0,2,-2,12,-24,...] is A052856(n-1)=[0,2,4,14,76,...]. - Michael Somos Mar 04 2004
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LINKS
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INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 557
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FORMULA
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Recurrence: {a(0)=0, a(1)=2, a(2)=2, (-2-n^2-3*n)*a(n)+a(n+2)}
Sum(1/2*(2+_alpha)*_alpha^(-1-n), _alpha=RootOf(-1+_Z^2))*n!
E.g.f.: x(x+2)/(1-x^2). a(2n+1)=2(2n+1)!. a(2n)=(2n)!, if n>0.
n! if n is even, 2n! otherwise.
a(n) = n! / gcd(n, tri(n)) where tri(n) is the n-th triangle number. - Andrew Plewe (aplewe(AT)sbcglobal.net), Jan 09 2006
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MAPLE
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spec := [S, {S=Prod(Z, Union(Sequence(Z), Sequence(Prod(Z, Z))))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
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PROGRAM
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(PARI) a(n)=if(n<0, 0, n!*polcoeff((x^2+2*x)/(1-x^2)+x*O(x^n), n))
(PARI) a(n)=if(n<1, 0, n!*(n%2+1))
(PARI) tri(n) = (n * (n + 1)) / 2 rclu(n) = n! / gcd(n, tri(n)) (Plewe)
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CROSSREFS
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Sequence in context: A122007 A137782 A131384 this_sequence A130306 A093044 A033886
Adjacent sequences: A052609 A052610 A052611 this_sequence A052613 A052614 A052615
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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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