A374626 Expansion of Product_{k>=0} 1 / (1 - 3*x^(3^k)).

1, 3, 9, 30, 90, 270, 819, 2457, 7371, 22143, 66429, 199287, 597951, 1793853, 5381559, 16144947, 48434841, 145304523, 435914388, 1307743164, 3923229492, 11769690933, 35309072799, 105927218397, 317781662562, 953344987686, 2860034963058, 8580104911317

Offset: 0

Author

Seiichi Manyama, Jul 14 2024

Keywords

• nonn

Crossrefs

For generating functions Product_{k>=0} 1 / (1 - a*x^(b^k)) for the following values of (a,b) see: (1,2) A018819, (1,3) A062051, (2,2) A309728.

Cf. A117940.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(1/prod(k=0, logint(N,3), 1-3*x^3^k))

Formula

G.f. A(x) satisfies A(x) = A(x^3)/(1 - 3*x).

a(n) is divisible by 3 for n > 0.