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%I #7 Dec 10 2020 16:47:04
%S 1,1,0,0,0,0,0,0,0,0,0,6,24,0,0,0,0,0,0,0,0,0,0,0,24,120,0,0,0,0,24,
%T 144,144,120,0,0,0,24,240,720,0,0,0,120,720,240,1440,0,0,0,840,5760,
%U 720,5160,744,240,720,1440,10080,720,5760,5160,1560,5760,2280,16560,6000,7560
%N Number of compositions (ordered partitions) of n into distinct parts such that the sum of reciprocals of parts is an integer.
%C Also the number of ordered ways to express an integer as the sum of distinct unit fractions such that the sum of the denominators is n.
%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%H <a href="/index/Ed#Egypt">Index entries for sequences related to Egyptian fractions</a>
%e a(11) = 6 because we have 2 + 3 + 6 = 2 + 6 + 3 = 3 + 2 + 6 = 3 + 6 + 2 = 6 + 2 + 3 = 6 + 3 + 2 = 11 and 1/2 + 1/3 + 1/6 = 1 is an integer.
%Y Cf. A051907, A051908, A058360, A339627, A339629.
%K nonn
%O 0,12
%A _Ilya Gutkovskiy_, Dec 10 2020
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