A071209 Triangular array T(n,k) read by rows, giving number of labeled free trees such that the root is smaller than all its children, with respect to the number n of vertices and to the size k of the subtree rooted at the vertex labeled by 1.

0, 1, 1, 0, 3, 8, 3, 0, 16, 81, 32, 18, 0, 125, 1024, 405, 240, 160, 0, 1296, 15625, 6144, 3645, 2560, 1875, 0, 16807, 279936, 109375, 64512, 45360, 35000, 27216, 0, 262144, 5764801, 2239488, 1312500, 917504, 708750, 580608, 470596, 0, 4782969

Offset: 1

Author

Cedric Chauve (chauve(AT)lacim.uqam.ca), May 16 2002

Keywords

• easy
• nonn
• tabl

References

• C. Chauve, S. Dulucq and O. Guibert, Enumeration of some labeled trees, Proceedings of FPSAC/SFCA 2000 (Moscow), Springer, pp. 146-157.

Links

• C. Chauve, S. Dulucq and O. Guibert, Enumeration of some labeled trees

Crossrefs

Cf. A000312.

Programs

Maple

(n,k) -> binomial(n,k-1)*k^(k-2)*(n-k)^(n+1-k);

PARI

tabl(nn) = {for (n=1, nn, for (k=1, n, print1(binomial(n, k-1)*k^(k-2)*(n-k)^(n+1-k), ", ");); print(););} \\ Michel Marcus, Jun 27 2013

Formula

binomial(n, k-1)*k^(k-2)*(n-k)^(n+1-k)