OFFSET
2,2
COMMENTS
T(n, k) is the number of forests of n - k edges that connect every other labeled vertex to one of the k roots (see Section 3 in Wästlund).
REFERENCES
Alfred Rényi, Some remarks on the theory of trees. MTA Mat. Kut. Inst. Kozl. (Publ. math. Inst. Hungar. Acad. Sci) 4 (1959), 73-85.
LINKS
Arthur Cayley, A theorem on trees, Quart. J. Pure Appl. Math. 23: 376-378 (1889). Also in The collected mathematical papers of Arthur Cayley vol 13.
John Riordan, Forests of labeled trees, Journal of Combinatorial Theory 5 (1968), 93-103.
Lajos Takács, On Cayley’s Formula for Counting Forests, Journal of Combinatorial Theory Series A 53, 321-323 (1990). See Equation 1.
Johan Wästlund, Padlock Solitaire: A martingale trick for combinatorial enumeration, arXiv:2008.13017 [math.CO], 2020. See Section 3.
MATHEMATICA
Table[k*n^(n-k-1), {n, 2, 11}, {k, 1, n-1}]//Flatten
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Stefano Spezia, Oct 20 2020
STATUS
approved