The corresponding article has been published in
Sitz.ber. d. ÖAW Math.-naturwiss. Klasse 198 (1989), 87-107.
Christian Krattenthaler
Counting lattice paths with a linear boundary I
Abstract.
Lattice paths in the plane that do not touch a given line are counted
with respect to four different statistics, which were introduced by
J. Fürlinger and J. Hofbauer (J. Combin. Theory Ser. A 40 (1985),
248-264) and generalize the well-known descent-major statistics. We give
generating functions, recurrence relations, and convolution identities
for the resulting numbers, which are generalizations of the well-known
Gould numbers A n(a,b) = a/(a+bn)
\binom {a+bn} {n}.
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