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%I #7 Aug 22 2019 20:33:33
%S 1,2,3,6,5,10,15,30,8,16,24,48,40,80,120,240,13,26,39,78,65,130,195,
%T 390,104,208,312,624,520,1040,1560,3120,21,42,63,126,105,210,315,630,
%U 168,336,504,1008,840,1680,2520,5040,273,546,819,1638,1365,2730,4095,8190
%N If n = Sum (2^e_k) then a(n) = Product (Fibonacci(e_k + 3)).
%F G.f.: Product_{k>=0} (1 + Fibonacci(k + 3) * x^(2^k)).
%F a(0) = 1; a(n) = Fibonacci(floor(log_2(n)) + 3) * a(n - 2^floor(log_2(n))).
%F a(2^(k-2)-1) = A003266(k).
%e 23 = 2^0 + 2^1 + 2^2 + 2^4 so a(23) = Fibonacci(3) * Fibonacci(4) * Fibonacci(5) * Fibonacci(7) = 390.
%t nmax = 55; CoefficientList[Series[Product[(1 + Fibonacci[k + 3] x^(2^k)), {k, 0, Floor[Log[2, nmax]] + 1}], {x, 0, nmax}], x]
%t a[0] = 1; a[n_] := Fibonacci[Floor[Log[2, n]] + 3] a[n - 2^Floor[Log[2, n]]]; Table[a[n], {n, 0, 55}]
%o (PARI) a(n)={vecprod([fibonacci(k+2) | k<-Vec(select(b->b, Vecrev(digits(n, 2)), 1))])} \\ _Andrew Howroyd_, Aug 19 2019
%Y Cf. A000045, A003266, A019565, A022290, A029930, A121663, A160009.
%K nonn
%O 0,2
%A _Ilya Gutkovskiy_, Aug 19 2019
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