0,8

Conjecture: polynomials with (positive) Fibonomial coefficients are reducible iff n odd >1. - Ralf Stephan, Oct 29 2004

Paul Barry, On Integer-Sequence-Based Constructions of Generalized Pascal Triangles, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.4.

A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A. 2003, p. 15.

A. Brousseau, Fibonacci and Related Number Theoretic Tables. Fibonacci Association, San Jose, CA, 1972.

D. E. Knuth, The Art of Computer Programming. Addison-Wesley, Reading, MA, Vol. 1, p. 84 and 492.

T. D. Noe, Rows n=0..50 of triangle, flattened

E. Krot, Further developments in Fibonomial calculus

E. Krot, An introduction to finite Fibonomial calculus

T. M. Richardson, The Filbert Matrix, arXiv:math/9905079

R. Stephan, A recurrence for the fibonomials

Eric Weisstein's World of Mathematics, Fibonacci Coefficient

a(n, k) = ((n, k)) = F(n)*F(n-1)*...*F(n-k+1)/F(k)*F(k-1)*...*F(1), F(i) = Fibonacci numbers A000045.

First few rows of the triangle are:

1;

1, 1;

1, 1, 1;

1, 2, 2, 1;

1, 3, 6, 3, 1;

1, 5, 15, 15, 5, 1;

1, 8, 40, 60, 40, 8, 1;

...

f[n_, k_] := Product[ Fibonacci[n - j + 1]/Fibonacci[j], {j, k}]; Table[ f[n, i], {n, 0, 10}, {i, 0, n}] [From Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 04 2009]

Cf. A055870 (signed version of triangle). Row sums give A056569.

Columns include A000045, A001654, A001655, A001656, A001657, A001658, A056565, A056566, A056567.

Cf. A144712. [From Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 04 2009]

Sequence in context: A010358 A155865 A156133 this_sequence A055870 A088459 A007799

Adjacent sequences: A010045 A010046 A010047 this_sequence A010049 A010050 A010051

nonn,tabl,easy,nice

N. J. A. Sloane (njas(AT)research.att.com).