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The Fibonomial coefficients are all integers. Some special values are:
Fibonomial triangle
The Fibonomial coefficients (sequence A010048 in the OEIS) are similar to binomial coefficients and can be displayed in a triangle similar to Pascal's triangle. The first eight rows are shown below.
1
1
1
1
1
1
1
2
2
1
1
3
6
3
1
1
5
15
15
5
1
1
8
40
60
40
8
1
1
13
104
260
260
104
13
1
The recurrence relation
implies that the Fibonomial coefficients are always integers.
Dov Jarden proved that the Fibonomials appear as coefficients of an equation involving powers of consecutive Fibonacci numbers, namely Jarden proved that given any generalized Fibonacci sequence , that is, a sequence that satisfies for every then
for every integer , and every nonnegative integer .