A294850 Number of compositions (ordered partitions) of 1 into exactly 2*n+1 powers of 1/3.

1, 1, 10, 217, 8317, 487630, 40647178, 4561368175, 663134389930, 121218250616173, 27212315953140892, 7359774260167595035, 2360287411461166320775, 885627663284464131142801, 384376149675044501884907410, 191068288010770323577312291141

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..200

Formula

a(n) = [x^(3^n)] (Sum_{j=0..2*n+1} x^(3^j))^(2*n+1).

a(n) ~ c * d^n * n^(2*n + 3/2), where d = 0.28934785344292228780991..., c = 1.984098413887380996408... - Vaclav Kotesovec, Sep 20 2019

Example

a(0) = 1: [1].
a(1) = 1: [1/3,1/3,1/3].
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].

Crossrefs

Column k=2 of A294746.

Sequence in context: A243476 A305107 A374794 * A259189 A326208 A007698

Adjacent sequences: A294847 A294848 A294849 * A294851 A294852 A294853

Keyword

nonn

Author

Alois P. Heinz, Nov 09 2017

Status

approved