fibonomial weekend teaser

[Ralf Stephan]

et al,
I have found the following forms for the fibonomial coefficients:


A010048(n,3) =
%F A001655 (1/10) [F(3n+6) + 2(-1)^n*F(n+2) ].

A010048(n,4) =
%F A001656 (1/150) [L(4n+10) + 3(-1)^nL(2n+5) - 6 ].

A010048(n,5) =
%F A001657 (1/750) [F(5n+15) + 5(-1)^nF(3n+9) - 15F(n+3) ].

A010048(n,6) =
%F A001658 (1/30000) [L(6n+21) + 8(-1)^nL(4n+14) - 40L(2n+7) - 60(-1)^n ].


Some patterns are obvious. Can you continue for the next rows or even
give or (gasp!) prove a general formula that does not use multiplication
of F or L?

The next sequences would be A056565, A056566, A056567, A056568.


Regards,
ralf