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A108525
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Number of increasing ordered rooted trees with n generators.
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4
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1, 3, 27, 429, 9609, 277107, 9772803, 407452221, 19604840481, 1069202914083, 65177482634667, 4391636680582029, 324102772814580729, 25999541378465556627, 2252597527900572815763, 209625760563134613131421
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OFFSET
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1,2
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COMMENTS
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A generator is a leaf or a node with just one child.
In an increasing rooted tree, nodes are numbered and numbers increase as you move away from root.
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LINKS
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FORMULA
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A(x) = Series_Reversion( (log(1-x) + 7*log(1+x) + 2/(x-1))/4 + 1/2). - Vaclav Kotesovec, Feb 20 2014
a(n) ~ sqrt(4-sqrt(2)) * 2^(3*n-13/4) * n^(n-1) / (exp(n) * (4-4*sqrt(2)-log(2)+14*log(2-1/sqrt(2)))^(n-1/2)). - Vaclav Kotesovec, Feb 20 2014
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MATHEMATICA
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Rest[CoefficientList[InverseSeries[Series[(Log[1-x]+7*Log[1+x]+2/(x-1))/4+1/2, {x, 0, 20}], x], x]*Range[0, 20]!] (* Vaclav Kotesovec, Feb 20 2014 *)
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PROG
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(PARI) {a(n)=local(A=x); for(i=1, n, A=intformal((A-1)^2 * (1+A) /(1 - 4*A + 2*A^2)+O(x^n))); n!*polcoeff(A, n)};
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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