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A052746
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a(0) = 0; a(n) = (2*n)^(n-1), n > 0.
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10
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0, 1, 4, 36, 512, 10000, 248832, 7529536, 268435456, 11019960576, 512000000000, 26559922791424, 1521681143169024, 95428956661682176, 6502111422497947648, 478296900000000000000, 37778931862957161709568, 3189059870763703892770816, 286511799958070431838109696
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OFFSET
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0,3
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COMMENTS
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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.
Number of labeled rooted directed trees on n nodes.
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LINKS
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FORMULA
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E.g.f.: -1/2*W(-2*x), where W is Lambert's W function.
E.g.f. g(x) satisfies g(x) = x*exp(2*g(x)) and (1-2*g(x)) g'(x) = g(x).
a(n) = (2*n/(n-1)) * Sum_{j=1..n-1} binomial(n-1,j)*a(j)*a(n-j) for n >= 2. (End)
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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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MATHEMATICA
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terms = 19;
A[x_] = -1/2 LambertW[-2 x];
Join[{0}, Table[(2n)^(n-1), {n, 20}]] (* Harvey P. Dale, Dec 14 2020 *)
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PROG
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(Sage)[lucas_number1(n, 2*n, 0) for n in range(0, 17)] # Zerinvary Lajos, Mar 09 2009
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CROSSREFS
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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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STATUS
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approved
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