OFFSET
0,2
FORMULA
a(n) ~ 2 * n^n * (1 + 4/n + 14/n^2 + 44/n^3 + 124/n^4 + 328/n^5 + 824/n^6 + 1980/n^7 + 4590/n^8 + 10320/n^9 + 22584/n^10 + ...), for coefficients see A261451. - Vaclav Kotesovec, Mar 05 2018
EXAMPLE
The table of coefficients of x^k in expansion of Product_{k>=1} ((1 + n*x^k)/(1 - n*x^k))^k begins:
n = 0: (1), 0, 0, 0, 0, 0, ...
n = 1: 1, (2), 6, 16, 38, 88, ...
n = 2: 1, 4, (16), 60, 192, 596, ...
n = 3: 1, 6, 30, (144), 582, 2280, ...
n = 4: 1, 8, 48, 280, (1376), 6568, ...
n = 5: 1, 10, 70, 480, 2790, (15800), ...
MATHEMATICA
Table[SeriesCoefficient[Product[((1 + n x^k)/(1 - n x^k))^k, {k, 1, n}], {x, 0, n}], {n, 0, 19}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Mar 05 2018
STATUS
approved