|
%I #8 Jan 18 2020 03:13:42
%S 1,0,1,1,5,1,24,1,55,19,128,1,1627,1,741,449,5271,1,45315,1,83343,
%T 3320,29966,1,5105721,571,200389,26425,5469758,1,154004510,1,47350055,
%U 226019,9262156,51885,15140335649,1,63346597,2044894,14700095925,1,185493291000,1,35539518745,478164162
%N Number of compositions (ordered partitions) of n into proper divisors of n.
%H Amiram Eldar, <a href="/A294138/b294138.txt">Table of n, a(n) for n = 0..3359</a>
%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%F a(n) = [x^n] 1/(1 - Sum_{d|n, d < n} x^d).
%F a(n) = A100346(n) - 1.
%e a(4) = 5 because 4 has 3 divisors {1, 2, 4} among which 2 are proper divisors {1, 2} therefore we have [2, 2], [2, 1, 1], [1, 2, 1], [1, 1, 2] and [1, 1, 1, 1].
%t Table[d = Divisors[n]; Coefficient[Series[1/(1 - Sum[Boole[d[[k]] != n] x^d[[k]], {k, Length[d]}]), {x, 0, n}], x, n], {n, 0, 45}]
%Y Cf. A027750, A032741, A065205, A100346, A210442, A294137.
%K nonn
%O 0,5
%A _Ilya Gutkovskiy_, Oct 23 2017
|
