A339651 Number of trees with n integer labeled leaves spanning an initial interval of positive integers and all non-leaf nodes having degree 3.

1, 1, 2, 4, 14, 92, 884, 11200, 175460, 3264456, 70251004, 1715832180, 46881727360, 1416695166888, 46909359288468, 1688908328539092, 65689047712686678, 2744769306400145168, 122618498876673122160, 5832010466617354498700, 294228096306408399225374

Offset: 0

Author

Andrew Howroyd, Dec 14 2020

Keywords

• nonn

Links

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

Crossrefs

Row sums of A339650.

Cf. A319590 (rooted).

Programs

PARI

\\ here U(n,k) is k-th column of A339650 as a vector.
R(n, k)={my(v=vector(n)); v[1]=k; for(n=2, n, v[n]=sum(j=1, (n-1)\2, v[j]*v[n-j]) + if(n%2, 0, binomial(v[n/2]+1, 2))); v}
U(n, k)={my(g=x*Ser(R(n,k))); Vec(1 + g + (subst(g + O(x*x^(n\3)), x, x^3) - g^3)/3) }
seq(n)={sum(k=0, n, U(n, k)*sum(r=k, n, binomial(r, k)*(-1)^(r-k)) )}