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A300456 a(n) = [x^n] Product_{k=1..n} ((1 + x^k)/(1 - x^k))^(n^k). 3
1, 2, 16, 200, 3264, 65752, 1565744, 42878432, 1324344832, 45464289482, 1715228012048, 70471268834936, 3129746696619072, 149318596196238328, 7612660420021177200, 412865831480749700928, 23725813528034949148672, 1439701175150489313314864, 91967625580609006328344400, 6167733266497532499924699672 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
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
Sequence in context: A012683 A012677 A158212 * A370326 A036081 A303673
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Mar 06 2018
STATUS
approved

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Last modified March 29 09:59 EDT 2024. Contains 371268 sequences. (Running on oeis4.)