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Number of partitions of the n-th Lucas number into Lucas parts (beginning with 1) (A000204).
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%I #10 Jul 26 2017 09:31:28

%S 1,2,3,6,13,39,147,755,5230,50282,677730,13010007,359551127,

%T 14457741910,853120090801,74437567936635,9666377127590346,

%U 1878877762201043122,549363336929733878734,242695457366120511255070,16263199149257162654631846

%N Number of partitions of the n-th Lucas number into Lucas parts (beginning with 1) (A000204).

%H <a href="/index/Par#part">Index entries for related partition-counting sequences</a>

%F a(n) = [x^A000204(n)] Product_{k>=1} 1/(1 - x^A000204(k)).

%F a(n) = A067592(A000204(n)).

%e a(4) = 6 because Lucas(4) = 7 and we have [7], [4, 3], [4, 1, 1, 1], [3, 3, 1], [3, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1].

%t Rest[Table[SeriesCoefficient[Product[1/(1 - x^LucasL[k]), {k, 1, n}], {x, 0, LucasL[n]}], {n, 0, 21}]]

%Y Cf. A000204, A003263, A067592, A098641.

%K nonn

%O 1,2

%A _Ilya Gutkovskiy_, Jul 24 2017