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A036772
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Number of labeled rooted trees with a degree constraint: ((4*n)!/(24^n)) * binomial(4*n+1, n).
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3
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1, 5, 2520, 9909900, 150089940000, 6217438242015000, 574985352122181000000, 103753754577643425255000000, 33189544956070738228953960000000, 17517292900368819935211385551000000000, 14427024664929016470240101675459976000000000
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OFFSET
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0,2
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LINKS
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FORMULA
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Recurrence (with no interpolated zeros): -8 * (4*n + 1) * (4*n + 3)^2 * (2*n + 1)^2 * (4*n + 5) * a(n) + (81*n^2 + 162*n + 72) * a(n + 1) = 0 for n >= 0 with a(0) = 1.
E.g.f. (with interpolated zeros): Let G(x) = Sum_{n >= 0} a(n)*x^(4*n + 1)/(4*n + 1)!. Then the e.g.f. satisfies G(x) = x * (1 + G(x)^4/4!).
(End)
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MATHEMATICA
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Table[(4n)!/24^n Binomial[4n+1, n], {n, 0, 10}] (* Harvey P. Dale, Aug 10 2011 *)
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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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