A253014 a(n) = number of unlabeled rooted trees on n nodes with an odd number of endpoints.

1, 1, 1, 2, 4, 10, 24, 58, 142, 359, 919, 2384, 6240, 16487, 43894, 117689, 317400, 860585, 2344280, 6413109, 17610746, 48527584, 134141036, 371862499, 1033586232, 2879818131, 8041864259, 22503532974, 63093269641, 177213423131

Offset: 1

Author

Marko Riedel, Dec 25 2014

Keywords

• nonn

Links

• 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

Crossrefs

Cf. A000081, A253013.

Programs

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;