Three closed forms for convolved Fibonacci numbers
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Keywords:
closed form; convolved Fibonacci number; Faà di Bruno formula; Bell polynomial of the second kind; higher order derivative; generating function; falling factorial; rising factorial; Lah number; Stirling number of the rst kind; golden ratio.Abstract
In the paper, by virtue of the Faà di Bruno formula and several properties of the Bell polynomials of the second kind, the author computes higher order derivatives of the generating function of convolved Fibonacci numbers and, consequently, derives three closed forms for convolved Fibonacci numbers in terms of the falling and rising factorials, the Lah numbers, the signed Stirling numbers of the rst kind, and the golden ratio.
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Published
2022-11-07
How to Cite
Feng Qi. (2022). Three closed forms for convolved Fibonacci numbers. Results in Nonlinear Analysis, 3(4), 185–195. Retrieved from https://nonlinear-analysis.com/index.php/pub/article/view/57
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