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

1,5

References

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

Links

Table of n, a(n) for n=1..44.

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

Formula

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

Maple

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

Prog

(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

Crossrefs

Cf. A000312.

Sequence in context: A245171 A011230 A245168 * A156227 A021727 A309648

Adjacent sequences: A071206 A071207 A071208 * A071210 A071211 A071212

Keyword

easy,nonn,tabl

Author

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

Status

approved