A253013 a(n) = number of unlabeled rooted trees on n nodes with an even number of endpoints.

0, 0, 1, 2, 5, 10, 24, 57, 144, 360, 923, 2382, 6246, 16486, 43917, 117692, 317447, 860574, 2344396, 6413119, 17611086, 48527597, 134141819, 371862485, 1033588413, 2879818379, 8041870070, 22503533295, 63093284667, 177213424466

Offset

1,4

Links

Table of n, a(n) for n=1..30.

F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973; see pp. 51-55.

Marko Riedel, Unlabled rooted trees with even and odd numbers of endpoints

Maple

T :=
proc(n)
    option remember;
    local k, s, A;
    if n=0 then return 0 fi;
    if n=1 then return u fi;
    A := n -> add(subs(u=u^l, T(n/l))/l,
                  l in divisors(n));
    s := (1-u)*A(n-1);
    s := s + 1/(n-1)*
    add((k+1)*A(k+1)*T(n-1-k), k=0..n-2);
    expand(s);
end;

Crossrefs

Cf. A000081, A253014.

Sequence in context: A359068 A151514 A321007 * A192471 A001431 A324149

Adjacent sequences: A253010 A253011 A253012 * A253014 A253015 A253016

Keyword

nonn

Author

Marko Riedel, Dec 25 2014

Status

approved