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A339781
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Number of homeomorphically irreducible trees with n integer labeled leaves covering an initial interval of positive integers.
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2
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1, 1, 2, 4, 22, 184, 2278, 37076, 747830, 17938120, 498221046, 15716127456, 554857740936, 21672428437044, 927792029298550, 43195423181912812, 2172838098801762500, 117433517088859845912, 6786305674234003471552, 417560119759063983102136, 27254276361313006814819076
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OFFSET
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0,3
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COMMENTS
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Homeomorphically irreducible trees are trees without vertices of degree 2.
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LINKS
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PROG
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(PARI)
EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
R(n, k)={my(v=[k]); for(n=2, n, v=concat(v, EulerT(concat(v, [0]))[n])); v}
U(n, k)={my(g=x*Ser(R(n, k))); Vec(1 + g + k*x*g - g^2)}
seq(n)={sum(k=0, n, U(n, k)*sum(r=k, n, binomial(r, k)*(-1)^(r-k)) )}
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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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