A094221 1/detM(n) where M(n) is the n X n matrix m(i,j)=F(i)/F(i+j-1) and F(i)=i-th Fibonacci number.

1, -2, -180, 2808000, 63248290560000, -13040516214928232110080000, -173699422048124050990739961787485511680000, 1013027110717881203216509560866301885575342298295136595148800000

Offset: 1

Author

Benoit Cloitre, May 28 2004

Keywords

• sign

Crossrefs

Cf. A062381.

Programs

Mathematica

Table[(-1)^Floor[n/2] * Product[Fibonacci[k]^k,{k,1,n-1}] * Product[Fibonacci[k]^(2*n-k),{k,n,2*n-1}] / Product[Fibonacci[k],{k,1,n}] / Product[Product[Fibonacci[k],{k,1,j-1}],{j,1,n}]^2,{n,1,10}] (* Vaclav Kotesovec, May 01 2015 *)

PARI

a(n)=1/matdet(matrix(n,n,i,j,fibonacci(i)/(fibonacci(i+j-1))))

Formula

a(n) = A062381(n)/A003266(n). - corrected by Vaclav Kotesovec, May 01 2015

a(n) ~ (-1)^floor(n/2) * A253270 * ((1+sqrt(5))/2)^(n*(4*n^2 - 3*n - 1)/6) / (A253267^2 * A062073^(2*n-1)). - Vaclav Kotesovec, May 01 2015