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Search: id:A138013
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| A138013 |
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E.g.f. satisfies A(x) = 1 - log(1 - x*A(x)). |
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+0
1
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| 1, 1, 3, 17, 146, 1694, 24834, 440586, 9180800, 219829536, 5948287560, 179508872520, 5978006444112, 217772950035120, 8614798644364080, 367768502385434640, 16852524904388586240, 825075552824125305600
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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a(n) = A038037(n+1)/(n+1) for n>=0 where A038037(n) is the number of labeled
rooted compound windmills (mobiles) with n nodes.
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FORMULA
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E.g.f.: A(x) = (1/x)*Series_Reversion[ x/(1 - log(1-x)) ]. E.g.f. satisfies exp(1 - A(x)) = 1 - x*A(x).
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EXAMPLE
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E.g.f.: A(x) = 1 + x + 3x^2/2! + 17x^3/3! + 146x^4/4! + 1694x^5/5! + ...
where A(x) = 1 - log(1 - x*A(x)):
A(x) = 1 + x*A(x) + x^2*A(x)^2/2 + x^3*A(x)^3/3 +...+ x^n*A(x)^n/n +...
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PROGRAM
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(PARI) {a(n)=n!*polcoeff(serreverse(x/(1-log(1-x + x^2*O(x^n) ))), n+1)}
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CROSSREFS
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Cf. A038037.
Adjacent sequences: A138010 A138011 A138012 this_sequence A138014 A138015 A138016
Sequence in context: A051442 A015735 A140983 this_sequence A052807 A080253 A009813
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Feb 27 2008
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