%I #25 Aug 01 2021 03:42:38

%S 1,2,3,5,6,8,13,15,21,34,40,55,60,89,104,144,233,260,273,377,610,714,

%T 987,1092,1597,1820,1870,2584,4181,4641,4895,6765,10946,12376,12816,

%U 17711,19635,28657,33552,46368,75025,83215,85085,87841,121393,136136

%N Ordered sequence of Fibonomial coefficients.

%C All Fibonacci numbers are present except 0. Members which are not Fibonacci numbers: A171159. (* _Robert G. Wilson v_, Dec 04 2009 *)

%H Robert G. Wilson v, <a href="/A144712/b144712.txt">Table of n, a(n) for n = 1..88</a>

%H D. E. Knuth and H. S. Wilf, <a href="http://dx.doi.org/10.1515/crll.1989.396.212">The Power of a Prime that Divides a Generalized Binomial Coefficient</a>, J. Reine Angew. Math. 396 (1989), 212-219.

%H Édouard Lucas, <a href="http://www.jstor.org/stable/2369308">Théorie des Fonctions Numériques Simplement Périodiques</a>, American J. Math. 1 (1878), 184-240, 289--321.

%H Édouard Lucas, <a href="http://www.mathstat.dal.ca/FQ/Books/Complete/simply-periodic.pdf">The Theory of Simply Periodic Numerical Functions</a>, Fibonacci Association, 1969. English translation of article "Théorie des Fonctions Numériques Simplement Périodiques, I", Amer. J. Math., 1 (1878), 184-240.

%H Diego Marques and Pavel Trojovsky, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL15/Trojovsky/trojovsky2.html">On Divisibility of Fibonomial Coefficients by 3</a>, Journal of Integer Sequences, Vol. 15 (2012), #12.6.4.

%F {[n,k]_F = (F_n...F_{n-k+1})/(F_1...F_k),n,k integers} = {f_1 < f_2 < f_3 < ...}

%e f_1=1, f_2=2, f_3=3, f_4=5, f_5=6.

%t f[n_, k_] := Product[Fibonacci[n - j + 1]/Fibonacci[j], {j, k}]; Take[ Union@ Flatten@ Table[ f[n, i], {n, 0, 27}, {i, 0, n}], 47] (* _Robert G. Wilson v_, Dec 04 2009 *)

%Y Cf. A010048. - _Robert G. Wilson v_, Dec 04 2009

%K nonn

%O 1,2

%A Florian Luca and Pante Stanica (pstanica(AT)nps.edu), Sep 19 2008

%E a(16)-a(47) from _Robert G. Wilson v_, Dec 04 2009