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%I #10 Sep 20 2019 05:37:22
%S 1,1,10,217,8317,487630,40647178,4561368175,663134389930,
%T 121218250616173,27212315953140892,7359774260167595035,
%U 2360287411461166320775,885627663284464131142801,384376149675044501884907410,191068288010770323577312291141
%N Number of compositions (ordered partitions) of 1 into exactly 2*n+1 powers of 1/3.
%H Alois P. Heinz, <a href="/A294850/b294850.txt">Table of n, a(n) for n = 0..200</a>
%F a(n) = [x^(3^n)] (Sum_{j=0..2*n+1} x^(3^j))^(2*n+1).
%F a(n) ~ c * d^n * n^(2*n + 3/2), where d = 0.28934785344292228780991..., c = 1.984098413887380996408... - _Vaclav Kotesovec_, Sep 20 2019
%e a(0) = 1: [1].
%e a(1) = 1: [1/3,1/3,1/3].
%e a(2) = 10: [1/3,1/3,1/9,1/9,1/9], [1/3,1/9,1/3,1/9,1/9], [1/3,1/9,1/9,1/3,1/9], [1/3,1/9,1/9,1/9,1/3], [1/9,1/3,1/3,1/9,1/9], [1/9,1/3,1/9,1/3,1/9], [1/9,1/3,1/9,1/9,1/3], [1/9,1/9,1/3,1/3,1/9], [1/9,1/9,1/3,1/9,1/3], [1/9,1/9,1/9,1/3,1/3].
%Y Column k=2 of A294746.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Nov 09 2017
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