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- Wolfdieter Lang
- 2000

Sequences of generalized Stirling numbers of both kinds are introduced. These sequences of triangles (i.e. infinite-dimensional lower triangular matrices) of numbers will be denoted by S2(k; n, m) and S1(k; n, m) with k ∈ Z. The original Stirling number triangles of the second and first kind arise when k = 1. turns out to be Catalan's triangle. Generating… (More)

- Wolfdieter Lang
- 2000

- Wolfdieter Lang
- 2009

A combinatorial interpretation of the earlier studied generalized Stirling numbers, emerging in a normal ordering problem and its inversion, is given. It involves unordered forests of certain types of labeled trees. Partition number arrays related to such forests are also presented.

- Wolfdieter Lang
- 2001

- Wolfdieter Lang
- 2000

1. WTMOBUCTION AND SUMMARY In [3] it has been shown that powers of the generating function c(x) of Catalan numbers {QaeNo = ft ^ > • • • } (m-1 4 5 9 a n d A000108 of [8] and references of [3]) can be expressed in terms of a linear combination of 1 and c(x) with coefficients replaced by certain scaled Chebyshev polynomials of the second kind. In this paper,… (More)

- Wolfdieter Lang
- 2014

Motivated by recent work of Trümper, we consider the general Collatz word (up-down pattern) and the sequences following this pattern. We derive recurrences for the first and last sequence entries from repeated application of the general solution of a binary linear inhomogeneous Diophantine equation. We solve these recurrences and also discuss the Collatz… (More)

- Wolfdieter Lang
- 1990

To my mother on the occasion of her 70th birthday. 1. Summary We consider the following three-term recursion formula (1.1a) 5_! = 0, S Q = 1 (1.1b) S n = Y(n)S n _ l-S n. 2 , n > 1 (1.1c) Yin) = Yh{n) + 2/(1-h(n)), (1. 2) h(n) = [ (n + 1)<|>].-[ft(j>]-1, where [a] denotes the integer part of a real number a, and cj): = (1 + /5)/2 5 obeying (j) 2 = < J > +… (More)

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