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

1, 1, 35, 4245, 1239823, 709097481, 701954099115, 1104353764428365, 2594884910993019575, 8684483842898500680225, 39880061006390454401626995, 243797643642188511890409843525, 1935230187172759446730224649089055, 19533122859042054951154895127392582265

Offset: 0

Author

Alois P. Heinz, Nov 09 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..165

Crossrefs

Column k=3 of A294746.

Formula

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

a(n) ~ c * d^n * n^(3*n + 3/2), where d = 0.228881755274644937676549309..., c = 3.08458888791535695636629... - Vaclav Kotesovec, Sep 20 2019