A071211 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 label k of the root.

1, 3, 1, 16, 8, 3, 125, 75, 40, 16, 1296, 864, 540, 300, 125, 16807, 12005, 8232, 5292, 3024, 1296, 262144, 196608, 143360, 100352, 65856, 38416, 16807, 4782969, 3720087, 2834352, 2099520, 1492992, 995328, 589824, 262144, 100000000

Offset

1,2

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..37.

Formula

T(n,k) = (n-k)*(n+1)^(n-k-1)*n^(k-1).

Maple

T:= (n, k)-> (n-k)*(n+1)^(n-k-1)*n^(k-1):
seq(seq(T(n, k), k=0..n-1), n=1..10);

Prog

(PARI) tabl(nn) = {for (n=1, nn, for (k=0, n-1, print1((n-k)*(n+1)^(n-k-1)*n^(k-1), ", "); ); print(); ); } \\ Michel Marcus, Jun 27 2013

Crossrefs

Cf. A000312, A000272 (first column).

Sequence in context: A143018 A102012 A128249 * A222029 A038675 A264902

Adjacent sequences: A071208 A071209 A071210 * A071212 A071213 A071214

Keyword

easy,nonn,tabl

Author

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

Status

approved