A300456 a(n) = [x^n] Product_{k=1..n} ((1 + x^k)/(1 - x^k))^(n^k).

1, 2, 16, 200, 3264, 65752, 1565744, 42878432, 1324344832, 45464289482, 1715228012048, 70471268834936, 3129746696619072, 149318596196238328, 7612660420021177200, 412865831480749700928, 23725813528034949148672, 1439701175150489313314864, 91967625580609006328344400, 6167733266497532499924699672

Offset

0,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..377

Formula

a(n) ~ exp(2*sqrt(2*n) - 1) * n^(n - 3/4) / (2^(3/4)*sqrt(Pi)). - Vaclav Kotesovec, Aug 26 2019

Example

The table of coefficients of x^k in expansion of Product_{k>=1} ((1 + x^k)/(1 - x^k))^(n^k) begins:
n = 0: (1),  0,    0,    0,     0,       0,  ...
n = 1:  1,  (2),   4,    8,    14,      24,  ...
n = 2:  1,   4,  (16),  60,   208,     692,  ...
n = 3:  1,   6,   36, (200), 1038,    5160   ...
n = 4:  1,   8,   64,  472, (3264),  21608,  ...
n = 5:  1,  10,  100,  920,  7950,  (65752), ...

Mathematica

Table[SeriesCoefficient[Product[((1 + x^k)/(1 - x^k))^(n^k), {k, 1, n}], {x, 0, n}], {n, 0, 19}]

Crossrefs

Cf. A015128, A252654, A261519, A261520, A270919, A270923, A270924, A292805, A300457, A300458.

Sequence in context: A012683 A012677 A158212 * A370326 A036081 A303673

Adjacent sequences: A300453 A300454 A300455 * A300457 A300458 A300459

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 06 2018

Status

approved