A General Lacunary Recurrence Formula

F. T. Howard

A chapter in Applications of Fibonacci Numbers, 2004, pp 121-135 from Springer

Abstract: Abstract The Bernoulli numbers B n may be defined by means of the generating function (1.1) $$ \frac{x}{{{e^{^x}} - 1}} = \sum\limits_{n = 0}^\infty {{B_n}} \frac{{{x^n}}}{{n!}} $$ . An example of a “lacuary” recurrence for these numbers is (1.2) $$ \sum\limits_{j = 0}^n {\left( \begin{array}{l}6n + 3 \\6j \\\end{array} \right)} {B_{6j}} = 2n + 1 $$ . This recurrence has lacunae, or gaps, or length 6. That is, to compute B 6n , it is not necessary to know the values of B j for all j

Keywords: 11B68; 11B39 (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1007/978-0-306-48517-6_13

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