|
%I M1607 #24 Jun 08 2019 01:09:37
%S 1,2,6,15,60,260,1820,12376,136136,1514513,27261234,488605194,
%T 14169550626,411591708660,19344810307020,908637119420910,
%U 69056421075989160,5249543573067466872,645693859487298425256,79413089729752455762384,15803204856220738696714416
%N Central Fibonomial coefficients.
%D A. Brousseau, Fibonacci and Related Number Theoretic Tables. Fibonacci Association, San Jose, CA, 1972, p. 74.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A. Brousseau, <a href="http://www.fq.math.ca/Scanned/6-1/brousseau3.pdf">A sequence of power formulas</a>, Fib. Quart., 6 (1968), 81-83.
%F a(n) = (Product_{k=floor(n/2)+1..n} Fibonacci(k)) / (Product_{k=1..ceiling(n/2)} Fibonacci(k)).
%F a(n) ~ ((1+sqrt(5))/2)^(n^2/4 + n + 1 - (1-(-1)^n)/8) / A062073, where A062073 = 1.2267420107203532444176302... is the Fibonacci factorial constant. - _Vaclav Kotesovec_, May 01 2015
%t Table[Product[Fibonacci[k],{k,Floor[n/2]+1,n}] / Product[Fibonacci[k],{k,1,Ceiling[n/2]}],{n,2,20}] (* _Vaclav Kotesovec_, Apr 10 2015 *)
%Y Central column of A010048, |A055870|.
%Y Cf. A062073.
%K nonn
%O 0,2
%A _N. J. A. Sloane_
%E More terms from _Vaclav Kotesovec_, May 01 2015
|
