A393556 Expansion of Product_{i>=1, j>=0} (1 + x^(i * 4^j)) / (1 - x^(i * 4^j)).

1, 2, 4, 8, 16, 28, 48, 80, 132, 210, 328, 504, 768, 1148, 1696, 2480, 3598, 5160, 7340, 10360, 14528, 20216, 27952, 38416, 52520, 71386, 96536, 129920, 174080, 232180, 308384, 407968, 537704, 706032, 923808, 1204688, 1565968, 2029132, 2621392, 3376720, 4337656

Offset

0,2

Comments

Convolution of A174065 and A373295.

Links

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

Formula

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

Mathematica

nmax = 50; CoefficientList[Series[Product[((1 + x^k)/(1 - x^k))^(IntegerExponent[k, 4] + 1), {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 50; CoefficientList[Series[Product[(1+x^(i*4^j))/(1-x^(i*4^j)), {i, 1, nmax}, {j, 0, Log[nmax]/Log[4]+1}], {x, 0, nmax}], x]

Crossrefs

Cf. A327727, A393555, A393557, A393558, A393559.

Cf. A174065, A373295.

Sequence in context: A276677 A112128 A208933 * A227036 A172020 A209410

Adjacent sequences: A393553 A393554 A393555 * A393557 A393558 A393559

Keyword

nonn

Author

Vaclav Kotesovec, Feb 21 2026

Status

approved