A071210 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 degree k of the root.

1, 3, 1, 18, 8, 1, 160, 80, 15, 1, 1875, 1000, 225, 24, 1, 27216, 15120, 3780, 504, 35, 1, 470596, 268912, 72030, 10976, 980, 48, 1, 9437184, 5505024, 1548288, 258048, 26880, 1728, 63, 1, 215233605, 127545840, 37200870, 6613488, 765450, 58320

Offset

1,2

Links

Table of n, a(n) for n=1..42.

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

Formula

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

Maple

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

Prog

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

Crossrefs

Cf. A000312, A052182 (first column).

Sequence in context: A370233 A335689 A105626 * A051141 A068141 A185025

Adjacent sequences: A071207 A071208 A071209 * A071211 A071212 A071213

Keyword

easy,nonn,tabl

Author

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

Status

approved