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Search: id:A052591
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| A052591 |
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A simple regular expression in a labeled universe. |
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+0
2
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| 0, 1, 2, 12, 48, 360, 2160, 20160, 161280, 1814400, 18144000, 239500800, 2874009600, 43589145600, 610248038400, 10461394944000, 167382319104000, 3201186852864000, 57621363351552000, 1216451004088320000
(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 2*a(n)=[2,4,24,96,...] is A052841(n+1)=[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 536
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FORMULA
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Recurrence: {a(1)=1, a(0)=0, (-n^3-5*n^2-8*n-4)*a(n)+(-2-n)*a(n+1)+(n+1)*a(n+2)}
(1/4*(-1)^(1-n)+1/2*n+1/4)*n!
E.g.f.: x/((1-x)(1-x^2)).
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MAPLE
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spec := [S, {S=Prod(Z, Sequence(Z), Sequence(Prod(Z, Z)))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
a:=n->(-1)*sum((-1)^k * (n-k+1) * n!, k=1..n) : seq(a(n), n=0..19); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 18 2007
a:=n->(n+1)!-sum((-1)^k*n!, k=0..n): seq(a(n)/2, 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/(1-x)/(1-x^2)+x*O(x^n), n))
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CROSSREFS
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Sequence in context: A048501 A001815 A052569 this_sequence A029766 A088311 A052588
Adjacent sequences: A052588 A052589 A052590 this_sequence A052592 A052593 A052594
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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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