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A253014 a(n) = number of unlabeled rooted trees on n nodes with an odd number of endpoints. 2
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 (list; graph; refs; listen; history; text; internal format)
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, A253013.

Sequence in context: A163271 A178036 A191625 * A110236 A191828 A065161

Adjacent sequences:  A253011 A253012 A253013 * A253015 A253016 A253017

KEYWORD

nonn

AUTHOR

Marko Riedel, Dec 25 2014

STATUS

approved

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Last modified September 21 21:32 EDT 2021. Contains 347605 sequences. (Running on oeis4.)