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Search: id:A052746
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| A052746 |
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a(0) = 0; a(n) = (2*n)^(n-1), n>0. |
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+0
7
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| 0, 1, 4, 36, 512, 10000, 248832, 7529536, 268435456, 11019960576, 512000000000, 26559922791424, 1521681143169024, 95428956661682176, 6502111422497947648, 478296900000000000000, 37778931862957161709568
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Expansion of inverse of x*exp(2x).
Number of well-colored directed trees on n nodes. Well-colored means, each green vertex has at least a red child, each red vertex has no red child.
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LINKS
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INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 702
C. Banderier, J.-M. Le Bars and V. Ravelomanana, Generating functions for kernels of digraphs
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FORMULA
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E.g.f.: -1/2*LambertW(-2*x)
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MAPLE
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spec := [S, {B=Set(S), S=Prod(Z, B, B)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
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PROGRAM
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(Other) SAGE:[lucas_number1(n, 2*n, 0) for n in xrange(0, 17)] [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 09 2009]
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CROSSREFS
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Cf. A038057.
Cf. A097627.
Sequence in context: A138435 A008546 A024253 this_sequence A145084 A098629 A070780
Adjacent sequences: A052743 A052744 A052745 this_sequence A052747 A052748 A052749
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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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EXTENSIONS
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New description from Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 08 2003
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