A003268 Central Fibonomial coefficients.

1, 2, 6, 15, 60, 260, 1820, 12376, 136136, 1514513, 27261234, 488605194, 14169550626, 411591708660, 19344810307020, 908637119420910, 69056421075989160, 5249543573067466872, 645693859487298425256, 79413089729752455762384, 15803204856220738696714416

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

References

• A. Brousseau, Fibonacci and Related Number Theoretic Tables. Fibonacci Association, San Jose, CA, 1972, p. 74.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• A. Brousseau, A sequence of power formulas, Fib. Quart., 6 (1968), 81-83.

Crossrefs

Central column of A010048, |A055870|.

Cf. A062073.

Programs

Mathematica

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 *)

Formula

a(n) = (Product_{k=floor(n/2)+1..n} Fibonacci(k)) / (Product_{k=1..ceiling(n/2)} Fibonacci(k)).

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

Extensions

More terms from Vaclav Kotesovec, May 01 2015