A339781 Number of homeomorphically irreducible trees with n integer labeled leaves covering an initial interval of positive integers.

1, 1, 2, 4, 22, 184, 2278, 37076, 747830, 17938120, 498221046, 15716127456, 554857740936, 21672428437044, 927792029298550, 43195423181912812, 2172838098801762500, 117433517088859845912, 6786305674234003471552, 417560119759063983102136, 27254276361313006814819076

Offset: 0

Author

Andrew Howroyd, Dec 16 2020

Keywords

• nonn

Comments

Homeomorphically irreducible trees are trees without vertices of degree 2.

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..200

Crossrefs

Row sums of A339780.

Programs

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)) )}