Ballots and trees

Cayley, 1889, A Theorem on Trees, Quart. J. Math. Oxford Ser. 2, 23, 376 Cayley, 1897, A Theorem on Trees, Collected Papers, Vol. 13, 26 Harris, 1952, First Passage and Recurrence Distributions, Trans. Amer. Math. Soc., 73, 471, 10.1090/S0002-9947-1952-0052057-2 Moon, 1967, Various Proofs of Cayley's Formula for Counting Trees Narayana, 1959, A Partial Order and Its Application to Probability Theory, Sankhyā Ser., 21, 91 Prüfer, 1918, Neuer Beweis eines Satzes über Permutationen, Arch. Math. Phys., 27, 742