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

0,3

Comments

Homeomorphically irreducible trees are trees without vertices of degree 2.

Links

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

Prog

(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)) )}

Crossrefs

Row sums of A339780.

Sequence in context: A283322 A019025 A264729 * A377358 A192332 A324603

Adjacent sequences: A339778 A339779 A339780 * A339782 A339783 A339784

Keyword

nonn

Author

Andrew Howroyd, Dec 16 2020

Status

approved