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

0,3

Links

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

Prog

(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)) )}

Crossrefs

Row sums of A339650.

Cf. A319590 (rooted).

Sequence in context: A181080 A166894 A232108 * A032052 A005737 A219767

Adjacent sequences: A339648 A339649 A339650 * A339652 A339653 A339654

Keyword

nonn

Author

Andrew Howroyd, Dec 14 2020

Status

approved