A361805 - OEIS

%I #31 Jan 29 2024 09:01:34

%S 1,2,10,52,278,1508,8262,45604,253186,1412196,7906866,44411420,

%T 250124308,1411963200,7986664250,45255888828,256840959728,

%U 1459686175768,8306130772008,47318321533008,269839722667800,1540242835509060,8799238591245006,50308756959106988

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

%H Vaclav Kotesovec, <a href="/A361805/b361805.txt">Table of n, a(n) for n = 0..1000</a>

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

%t 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}]

%Y Cf. A369577, A369578.

%Y Cf. A015128, A103265, A280263.

%Y Cf. A000041, A001156, A003108.

%Y Cf. A000009, A033461, A279329.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Jan 28 2024