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A144712 Ordered sequence of Fibonomial coefficients.

%I A144712 #28 Jul 28 2025 00:01:27
%S A144712 1,2,3,5,6,8,13,15,21,34,40,55,60,89,104,144,233,260,273,377,610,714,
%T A144712 987,1092,1597,1820,1870,2584,4181,4641,4895,6765,10946,12376,12816,
%U A144712 17711,19635,28657,33552,46368,75025,83215,85085,87841,121393,136136
%N A144712 Ordered sequence of Fibonomial coefficients.
%C A144712 All Fibonacci numbers are present except 0. Members which are not Fibonacci numbers: A171159. - _Robert G. Wilson v_, Dec 04 2009
%H A144712 Robert G. Wilson v, <a href="/A144712/b144712.txt">Table of n, a(n) for n = 1..88</a>
%H A144712 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 A144712 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 A144712 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 A144712 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 A144712 {[n,k]_F = (F_n...F_{n-k+1})/(F_1...F_k),n,k integers} = {f_1 < f_2 < f_3 < ...}
%e A144712 f_1=1, f_2=2, f_3=3, f_4=5, f_5=6.
%t A144712 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 A144712 Cf. A010048. - _Robert G. Wilson v_, Dec 04 2009
%K A144712 nonn
%O A144712 1,2
%A A144712 Florian Luca and Pante Stanica (pstanica(AT)nps.edu), Sep 19 2008
%E A144712 a(16)-a(47) from _Robert G. Wilson v_, Dec 04 2009