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%I #9 Apr 02 2020 11:43:58
%S 1,3,8,26,132,1058,13756,288878,9821854,540201972,48077975510,
%T 6923228473442,1613112234311988,608143312335619478,
%U 370967420524727881582,366144844057906419121436,584733315960476551336933294,1510950888441871408654635631698
%N A recursive sequence: a(n) = Fibonacci(n)*a(n-1) + 2.
%F a(n) ~ c * ((1+sqrt(5))/2)^(n^2/2+n/2) / 5^(n/2), where c = A062073 * (2*A101689-1) = 5.4087126382942177293... is product of Fibonacci factorial constant (see A062073) and -1+2*sum_{n>=1} 1/product(A000045(k), k=1..n).
%t RecurrenceTable[{a[n]==Fibonacci[n]*a[n-1]+2,a[1]==1},a,{n,1,20}]
%Y Cf. A176343, A238244, A003266, A101689, A062073, A000045, A139339.
%K nonn
%O 1,2
%A _Vaclav Kotesovec_, Feb 20 2014
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