Wolfdieter Lang

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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)
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)
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)
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)
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