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A005373
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A class of rooted trees with n nodes.
(Formerly M3083)
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4
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1, 3, 21, 231, 3495, 67455, 1584765, 43897455, 1400923755, 50619052575, 2042745514425, 91066568444775, 4444738893770175, 235731740255186175, 13499365993279291125, 830161812269496081375, 54564569247212367217875, 3817309552613869238301375
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OFFSET
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1,2
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COMMENTS
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See Table 3 on page 32 of the Felsenstein reference: "The numbers of rooted trees with n labelled species, allowing some interior nodes to be labelled, but allowing no more than two immediate descendants of each interior node." - Joerg Arndt, Jun 02 2016
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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a(n) = Sum_{m=1..n} Sum_{p=1..n-m} V(n,m,p) where V(1,0,0)=1, V(1,i,j)=0, and V(n,m,p) = [p>0]*((2*n-2*m-p-2)*V(n-1,m,p1) + (n-m-p)*V(n-1,m,p-1)) + [m>0]*((n-2*m-p)*V(n-1,m-1,p) + (p+1)*V(n-1,m-1,p+1)) + [2*n-2*m-p-3>0]*(2*n-2*m-p-3)*V(n-1,m,p) with [t>0]=1 if t>0 and 0 otherwise. - Sean A. Irvine, Jun 02 2016
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CROSSREFS
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KEYWORD
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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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