A302999 a(n) = Product_{k=1..n} (Fibonacci(k+2) - 1).
1, 1, 2, 8, 56, 672, 13440, 443520, 23950080, 2107607040, 301387806720, 69921971159040, 26290661155799040, 16011012643881615360, 15786858466867272744960, 25195826113120167300956160, 65080818850189392138369761280, 272037822793791659138385602150400
Offset: 0
Keywords
Examples
The matrix begins: 1 1 1 1 1 1 1 1 ... 1 2 1 1 1 1 1 1 ... 1 1 3 1 1 1 1 1 ... 1 1 1 5 1 1 1 1 ... 1 1 1 1 8 1 1 1 ... 1 1 1 1 1 13 1 1 ... 1 1 1 1 1 1 21 1 ... 1 1 1 1 1 1 1 34 ...
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..97
Programs
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Maple
b:= proc(n) b(n):= `if`(n<1, [1$2][], (f-> [f, b(n-1)[2]*(f-1)][])(b(n-1)+b(n-2))) end: a:= n-> b(n)[2]: seq(a(n), n=0..20); # Alois P. Heinz, Apr 24 2018 -
Mathematica
Table[Product[Fibonacci[k + 2] - 1, {k, 1, n}], {n, 0, 17}] Table[Product[Sum[Fibonacci[j], {j, 1, k}], {k, 1, n}], {n, 0, 17}] Table[Det[Table[If[i == j, Fibonacci[i + 1], 1], {i, 1, n + 1}, {j, 1, n + 1}]], {n, 0, 17}]
Formula
a(n) = Product_{k=1..n} A000071(k+2).
a(n) = Product_{k=1..n} Sum_{j=1..k} A000045(j).
a(n) ~ c * ((1 + sqrt(5))/2)^(n*(n+5)/2) / 5^(n/2), where c = 0.1972502311584232476952451740107000852343536766534965116633336539193... - Vaclav Kotesovec, Apr 17 2018
a(n) = A190535(n-3) for n > 3. - Alois P. Heinz, Apr 25 2018
Comments