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A052746
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a(0) = 0; a(n) = (2*n)^(n-1), n>0.
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6
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0, 1, 4, 36, 512, 10000, 248832, 7529536, 268435456, 11019960576, 512000000000, 26559922791424, 1521681143169024, 95428956661682176, 6502111422497947648, 478296900000000000000, 37778931862957161709568
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| 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
| 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
| E.g.f.: -1/2*W(-2*x), where W is Lambert's W function.
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MAPLE
| spec := [S, {B=Set(S), S=Prod(Z, B, B)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
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PROG
| (Other) SAGE:[lucas_number1(n, 2*n, 0) for n in xrange(0, 17)] [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 09 2009]
(PARI) a(n)=if(n, (2*n)^(n-1), 0) \\ Charles R Greathouse IV, Nov 20 2011
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CROSSREFS
| Cf. A038057, A097627.
Sequence in context: A138435 A008546 A024253 * A145084 A179422 A098629
Adjacent sequences: A052743 A052744 A052745 * A052747 A052748 A052749
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KEYWORD
| easy,nonn
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AUTHOR
| encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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EXTENSIONS
| New description from Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 08 2003
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