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# Fibonomial Coefficient

The fibonomial coefficient (sometimes also called simply the Fibonacci coefficient) is defined by

 (1)

where and is a Fibonacci number. This coefficient satisfies

 (2)

for , where is a Lucas number.

The triangle of fibonomial coefficients is given by

 (3)

(OEIS A010048).

may be called the central fibonomial coefficient by analogy with the central binomial coefficient.

Binomial Coefficient, Central Fibonomial Coefficient, Fibonacci Number, Fibonorial, Lucas Number

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## References

Benjamin, A. T. and Quinn, J. J. Proofs That Really Count: the Art of Combinatorial Proof. Washington, DC: Math. Assoc. Amer., p. 15, 2003.Brousseau, A. Fibonacci and Related Number Theoretic Tables. San Jose, CA: Fibonacci Association, 1972.Knuth, D. E. The Art of Computer Programming, Vol. 1: Fundamental Algorithms, 3rd ed. Reading, MA: Addison-Wesley, pp. 84 and 492, 1997.Krot, E. "Further Developments in Finite Fibonomial Calculus." 27 Oct 2004. http://arxiv.org/abs/math.CO/0410550.Richardson, T. M. "The Filbert Matrix." 12 May 1999. http://arxiv.org/abs/math/9905079.Sloane, N. J. A. Sequence A010048 in "The On-Line Encyclopedia of Integer Sequences."

## Referenced on Wolfram|Alpha

Fibonomial Coefficient

## Cite this as:

Weisstein, Eric W. "Fibonomial Coefficient." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/FibonomialCoefficient.html