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
Keywords
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
Programs
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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;
Comments