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A038034 Number of compositions (ordered partitions) of 1 into {1/1, 1/2, 1/3, ..., 1/n}. 5

%I #17 Dec 19 2015 10:57:17

%S 1,2,3,7,8,52,53,288,1209,5247,5248,71395,71396,375779,6957533,

%T 52310862,52310863,1152622553,1152622554,45575902465,1296407854551,

%U 1580527987951,1580527987952,73245316681199,584407520822198,639887219617512,11355804443049274,516959218512416104,516959218512416105,29213061562205847736,29213061562205847737,886912328033731357358,31286298736622399674197,31349361777225437765677

%N Number of compositions (ordered partitions) of 1 into {1/1, 1/2, 1/3, ..., 1/n}.

%C a(n) = number of Egyptian fractions 1 = 1/x_1 + ... + 1/x_k (for any k), with max{x_i}<=n.

%H <a href="/index/Ed#Egypt">Index entries for sequences related to Egyptian fractions</a>

%F a(n) = Sum_{i=1..n} A092667(i).

%e a(4) = 7 since there are seven compositions into parts {1/1, 1/2, 1/3, 1/4}:

%e 1 = 1/1, 1 = 1/2 + 1/2, 1 = 1/3 + 1/3 + 1/3, 1 = 1/2 + 1/4 + 1/4, 1 = 1/4 + 1/2 + 1/4, 1 = 1/4 + 1/4 + 1/2, and 1 = 1/4 + 1/4 + 1/4 + 1/4.

%Y Cf. A002967, A020473, A092667, A092670.

%K nonn,nice

%O 1,2

%A _Christian G. Bower_, Jun 15 1998

%E More terms from _Max Alekseyev_, Mar 02 2004

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Last modified March 29 02:13 EDT 2024. Contains 371264 sequences. (Running on oeis4.)