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A005373 A class of rooted trees with n nodes.
(Formerly M3083)
4
1, 3, 21, 231, 3495, 67455, 1584765, 43897455, 1400923755, 50619052575, 2042745514425, 91066568444775, 4444738893770175, 235731740255186175, 13499365993279291125, 830161812269496081375, 54564569247212367217875, 3817309552613869238301375 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
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
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
J. Felsenstein, The number of evolutionary trees, Systematic Zoology, 27 (1978), 27-33.
J. Felsenstein, The number of evolutionary trees, Systematic Zoology, 27 (1978), 27-33. (Annotated scanned copy)
FORMULA
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
CROSSREFS
Sequence in context: A119097 A326604 A008545 * A078586 A179331 A138903
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Sean A. Irvine, Jun 02 2016
STATUS
approved

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)