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A253014
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a(n) = number of unlabeled rooted trees on n nodes with an odd number of endpoints.
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2
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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
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OFFSET
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1,4
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LINKS
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MAPLE
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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;
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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