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Product_{k=1..n} Fibonacci(k)^k.
2

%I #10 Oct 17 2019 10:41:32

%S 1,1,8,648,2025000,530841600000,33309523161907200000,

%T 1259861409934788058133299200000,

%U 76494996113757662751632456649087438028800000,19375812441937279261781767910157290423127539712000000000000000

%N Product_{k=1..n} Fibonacci(k)^k.

%F a(n) ~ c * ((1+sqrt(5))/2)^(n*(n+1)*(2*n+1)/6) / 5^(n*(n+1)/4), where c = A253270 = 1.1188674438617789501735355690557711005492672642422237428157122531318... .

%t Table[Product[Fibonacci[k]^k,{k,1,n}],{n,1,10}]

%t FoldList[Times,Table[Fibonacci[n]^n,{n,10}]] (* _Harvey P. Dale_, Oct 17 2019 *)

%Y Cf. A000045, A003266, A062381, A152686, A253270.

%K nonn,easy

%O 1,3

%A _Vaclav Kotesovec_, May 01 2015