A361805 Expansion of Product_{j=1..n, k=1..n} (1 + x^(k^j)) / (1 - x^(k^j)).

1, 2, 10, 52, 278, 1508, 8262, 45604, 253186, 1412196, 7906866, 44411420, 250124308, 1411963200, 7986664250, 45255888828, 256840959728, 1459686175768, 8306130772008, 47318321533008, 269839722667800, 1540242835509060, 8799238591245006, 50308756959106988

Offset

0,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..1000

Formula

a(n) ~ c * (1 + sqrt(2))^(2*n) / sqrt(n), where c = 0.6431307610999754935775134585988078560575016233514072350040712130921818...

Mathematica

Table[SeriesCoefficient[Product[Product[(1+x^(k^j))/(1-x^(k^j)), {k, 1, n^(1/j)}], {j, 1, n}], {x, 0, n}], {n, 0, 40}]

Crossrefs

Cf. A369577, A369578.

Cf. A015128, A103265, A280263.

Cf. A000041, A001156, A003108.

Cf. A000009, A033461, A279329.

Sequence in context: A307208 A075436 A319325 * A344576 A360317 A074612

Adjacent sequences: A361802 A361803 A361804 * A361806 A361807 A361808

Keyword

nonn

Author

Vaclav Kotesovec, Jan 28 2024

Status

approved