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A294851 Number of compositions (ordered partitions) of 1 into exactly 3*n+1 powers of 1/4. 2

%I #6 Sep 20 2019 05:51:35

%S 1,1,35,4245,1239823,709097481,701954099115,1104353764428365,

%T 2594884910993019575,8684483842898500680225,

%U 39880061006390454401626995,243797643642188511890409843525,1935230187172759446730224649089055,19533122859042054951154895127392582265

%N Number of compositions (ordered partitions) of 1 into exactly 3*n+1 powers of 1/4.

%H Alois P. Heinz, <a href="/A294851/b294851.txt">Table of n, a(n) for n = 0..165</a>

%F a(n) = [x^(4^n)] (Sum_{j=0..3*n+1} x^(4^j))^(3*n+1).

%F a(n) ~ c * d^n * n^(3*n + 3/2), where d = 0.228881755274644937676549309..., c = 3.08458888791535695636629... - _Vaclav Kotesovec_, Sep 20 2019

%Y Column k=3 of A294746.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Nov 09 2017

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