Definition:Fibonomial Triangle

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Definition

The Fibonomial triangle is an array formed by the Fibonomial coefficients:


$\begin{array}{r|rrrrrrrrrr} n & \binom n 0_\FF & \binom n 1_\FF & \binom n 2_\FF & \binom n 3_\FF & \binom n 4_\FF & \binom n 5_\FF & \binom n 6_\FF \\ \hline 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & \\ 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & \\ 2 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & \\ 3 & 1 & 2 & 2 & 1 & 0 & 0 & 0 & \\ 4 & 1 & 3 & 6 & 3 & 1 & 0 & 0 & \\ 5 & 1 & 5 & 15 & 15 & 5 & 1 & 0 & \\ 6 & 1 & 8 & 40 & 60 & 40 & 8 & 1 & \\ \end{array}$

This sequence is A010048 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).


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