cp's OEIS Frontend

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

%I A339781 #9 Jan 10 2021 02:13:21
%S A339781 1,1,2,4,22,184,2278,37076,747830,17938120,498221046,15716127456,
%T A339781 554857740936,21672428437044,927792029298550,43195423181912812,
%U A339781 2172838098801762500,117433517088859845912,6786305674234003471552,417560119759063983102136,27254276361313006814819076
%N A339781 Number of homeomorphically irreducible trees with n integer labeled leaves covering an initial interval of positive integers.
%C A339781 Homeomorphically irreducible trees are trees without vertices of degree 2.
%H A339781 Andrew Howroyd, <a href="/A339781/b339781.txt">Table of n, a(n) for n = 0..200</a>
%o A339781 (PARI)
%o A339781 EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
%o A339781 R(n, k)={my(v=[k]); for(n=2, n, v=concat(v, EulerT(concat(v, [0]))[n])); v}
%o A339781 U(n, k)={my(g=x*Ser(R(n,k))); Vec(1 + g + k*x*g - g^2)}
%o A339781 seq(n)={sum(k=0, n, U(n, k)*sum(r=k, n, binomial(r, k)*(-1)^(r-k)) )}
%Y A339781 Row sums of A339780.
%K A339781 nonn
%O A339781 0,3
%A A339781 _Andrew Howroyd_, Dec 16 2020