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A029758
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Number of AVL trees of height n.
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4
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1, 1, 3, 15, 315, 108675, 11878720875, 141106591466142946875, 19911070158545297149037891328865229296875, 396450714858513044552818188364610837019719636049876979456842033610756600341796875
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OFFSET
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0,3
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REFERENCES
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D. E. Knuth, Art of Computer Programming, Vol. 3, Sect. 6.2.3 (7) and (8).
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LINKS
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FORMULA
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a(n+1) = a(n)^2 + 2*a(n)*a(n-1).
According to Knuth (p. 715), a(n) ~ c^(2^n), where c = 1.4368728483944618758004279843355486292481149448324679771230546290458819902268... - Vaclav Kotesovec, Dec 17 2018
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EXAMPLE
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G.f. = 1 + x + 3*x^2 + 15*x^3 + 315*x^4 + 108675*x^5 + 11878720875*x^6 + ...
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MAPLE
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MATHEMATICA
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a[0] = a[1] = 1; a[n_] := a[n] = a[n-1]^2 + 2*a[n-1]*a[n-2]; Table[a[n], {n, 0, 9}] (* Jean-François Alcover, Feb 13 2015 *)
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PROG
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(PARI) {a(n) = if( n<2, n>=0, a(n-1) * (a(n-1) + 2*a(n-2)))}; /* Michael Somos, Feb 07 2004 */
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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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EXTENSIONS
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STATUS
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approved
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