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%I #5 Aug 28 2017 17:45:30
%S 1,1,2,5,4,12,14,16,42,35,65,100,84,205,201,254,490,386,749,917,851,
%T 1816,1566,2260,3513,2784,5566,5748,6116,11366,9048,14740,19037,16095,
%U 31576,28505,35218,56334,43671,77512,85163,80577,147756,121016,172408,236022
%N Expansion of Product_{k>=2} (1 + x^Fibonacci(k))^Fibonacci(k).
%C Number of partitions of n into distinct Fibonacci parts (1 counted as single Fibonacci number), where Fibonacci(k) different parts of size Fibonacci(k) are available (1a, 2a, 2b, 3a, 3b, 3c, ...).
%H <a href="/index/Par#part">Index entries for related partition-counting sequences</a>
%F G.f.: Product_{k>=2} (1 + x^A000045(k))^A000045(k).
%e a(3) = 5 because we have [3a], [3b], [3c], [2a, 1a] and [2b, 1a].
%t nmax = 50; CoefficientList[Series[Product[(1 + x^Fibonacci[k])^Fibonacci[k], {k, 2, nmax}], {x, 0, nmax}], x]
%Y Cf. A000045, A000119, A000121, A026007, A166861, A200544, A239002, A260787, A261050.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Aug 28 2017
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