OFFSET
0,4
FORMULA
a(n) = n! * [x^n] exp(-n*Sum_{k>=1} d(k)*x^k/k), where d(k) is the number of divisors of k (A000005).
EXAMPLE
The table of coefficients of x^k in expansion of e.g.f. Product_{k>=1} (1 - x^k)^(n/k) begins:
n = 0: (1), 0, 0, 0, 0, 0, 0, ...
n = 1: 1, (-1), -1, 1, -1, 41, -131, ...
n = 2: 1, -2, (0), 8, -4, 72, -704, ...
n = 3: 1, -3, 3, (15), -45, 63, -1539, ...
n = 4: 1, -4, 8, 16, (-136), 224, -1856, ...
n = 5: 1, -5, 15, 5, -265, (885), -2075, ...
n = 6: 1, -6, 24, -24, -396, 2376, (-4896), ...
MATHEMATICA
Table[n! SeriesCoefficient[Product[(1 - x^k)^(n/k), {k, 1, n}], {x, 0, n}], {n, 0, 19}]
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Feb 01 2018
STATUS
approved