A003268 Central Fibonomial coefficients. (Formerly M1607)

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

Offset

0,2

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

Table of n, a(n) for n=0..20.

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

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

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 *)

Crossrefs

Central column of A010048, |A055870|.

Cf. A062073.

Sequence in context: A192186 A243550 A354758 * A242792 A216811 A351900

Adjacent sequences: A003265 A003266 A003267 * A003269 A003270 A003271

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Vaclav Kotesovec, May 01 2015

Status

approved