Generalization of a Formula of Touchard for Catalan Numbers
نویسنده
چکیده
منابع مشابه
Some Identities and Formulas Involving Generalized Catalan Numbers Siu-ah Ng
A generalization of the Catalan numbers is considered. New results include binomial identities, recursive relations and a close formula for the multivariate generating function. A simple expression for the Catalan determinant is derived.
متن کاملA Refinement of the Formula for k-ary Trees and the Gould-Vandermonde's Convolution
In this paper, we present an involution on some kind of colored k-ary trees which provides a combinatorial proof of a combinatorial sum involving the generalized Catalan numbers Ck,γ(n) = γ kn+γ ( kn+γ n ) . From the combinatorial sum, we refine the formula for k-ary trees and obtain an implicit formula for the generating function of the generalized Catalan numbers which obviously implies a Van...
متن کاملq-Catalan Numbers
q-analogs of the Catalan numbers c', = (I/(n + I))($) are studied from the viewpoint of Lagrange inversion. The first, due to Carhtz, corresponds to the Andrews-Gessel-Garsia q-Lagrange inversion theory, satisfies a nice recurrence relation and counts inversions of Catalan words. The second, tracing back to Mac Mahon, arise from Krattenthaler's and Gessel and Stanton's q-Lagrange inversion form...
متن کاملq-CATALAN IDENTITIES
q-Analogs of the Catalan number identities of Touchard, Jonah and Koshy are derived.
متن کاملThe Super Patalan Numbers
We introduce the super Patalan numbers, a generalization of the super Catalan numbers in the sense of Gessel, and prove a number of properties analogous to those of the super Catalan numbers. The super Patalan numbers generalize the super Catalan numbers similarly to how the Patalan numbers generalize the Catalan numbers.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 23 شماره
صفحات -
تاریخ انتشار 1977