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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.

- W H Lang, K E van Holde
- Proceedings of the National Academy of Sciences…
- 1991

A number of additional cDNA clones coding for portions of the very large polypeptide chain of Octopus dofleini hemocyanin were isolated and sequenced. These data reveal two very similar coding sequences, which we have denoted "A-type" and "G-type." We have obtained complete A-type sequences coding for functional units Ode and Odf; consequently a total of… (More)

- 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)

1. A table of previous descriptions of larvae of Diogenidae is given. 2. Larvae of the hermit crab Clibanarius vittatus were reared on a diet of Artemia nauplii. Five, rarely four, zoeal stages and megalopa were obtained. Duration, mortality and sizes of larvae from two hatches are listed. 3. Detailed descriptions and figures for each larval stage are… (More)

- Wolfdieter Lang, Saïd Amghibech
- The American Mathematical Monthly
- 2002

- Wolfdieter Lang
- The American Mathematical Monthly
- 2001

- 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)