A121709 Numerator of Sum/Product of first n Lucas numbers A000032[n].

1, 4, 2, 5, 13, 1, 73, 5, 7, 1, 37, 5, 1361, 1, 223, 25, 4673, 1, 24473, 25, 16019, 1, 83879, 65, 62743, 1, 20533, 65, 1505173, 1, 7881193, 85, 5158309, 1, 27009259, 425, 1400221, 1, 1446283, 2225, 69237359, 1, 51790217, 445, 1660959719, 1, 8696897999

Offset: 1

Author

Alexander Adamchuk, Aug 16 2006

Keywords

• frac
• nonn

Comments

5 divides a(4k). a(1) = 1 and a(4k+2) = 1 for k>0.

Crossrefs

Cf. A000045, A000032, A079451, A001578, A096362, A058036, A121708, A090585.

Programs

Mathematica

Table[Numerator[Sum[Fibonacci[k-1]+Fibonacci[k+1],{k,1,n}]/Product[Fibonacci[k-1]+Fibonacci[k+1],{k,1,n}]],{n,1,100}]

Formula

a(n) = Numerator[Sum[Lucas[k],{k,1,n}]/Product[Lucas[k],{k,1,n}]], where Lucas[k] = Fibonacci[k-1] + Fibonacci[k+1].