A393555 Expansion of Product_{i>=1, j>=0} (1 + x^(i * 3^j)) / (1 - x^(i * 3^j)).

1, 2, 4, 10, 18, 32, 60, 100, 164, 276, 436, 680, 1070, 1624, 2440, 3672, 5402, 7880, 11484, 16476, 23472, 33360, 46880, 65488, 91212, 125958, 173048, 237012, 322432, 436680, 589604, 791720, 1058948, 1412208, 1874708, 2479992, 3271596, 4299056, 5631536, 7357804

Offset

0,2

Comments

Convolution of A327726 and A173241.

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Formula

log(a(n)) ~ Pi*sqrt(3*n/2).

Mathematica

nmax = 50; CoefficientList[Series[Product[((1 + x^k)/(1 - x^k))^(IntegerExponent[k, 3] + 1), {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 50; CoefficientList[Series[Product[(1+x^(i*3^j))/(1-x^(i*3^j)), {i, 1, nmax}, {j, 0, Log[nmax]/Log[3]+1}], {x, 0, nmax}], x]

Crossrefs

Cf. A327727, A393556, A393557, A393558, A393559.

Cf. A327726, A173241.

Sequence in context: A375625 A045955 A182248 * A093695 A308529 A320098

Adjacent sequences: A393552 A393553 A393554 * A393556 A393557 A393558

Keyword

nonn

Author

Vaclav Kotesovec, Feb 21 2026

Status

approved