|
|
A298596
|
|
Expansion of Product_{k>=2} 1/(1 + x^k).
|
|
0
|
|
|
1, 0, -1, -1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, -1, 1, 0, 0, -1, 1, -1, 0, -1, 2, -1, 0, -2, 2, -1, 1, -2, 3, -2, 1, -3, 4, -2, 2, -4, 5, -3, 3, -5, 6, -5, 4, -6, 9, -6, 5, -9, 10, -8, 8, -11, 13, -11, 10, -14, 17, -14, 13, -19, 21, -18, 18, -23, 26, -24, 23, -29, 34, -30, 29, -38, 41, -38, 39
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,25
|
|
COMMENTS
|
The difference between the number of partitions of n into an even number of parts > 1 and the number of partitions of n into an odd number of parts > 1.
|
|
LINKS
|
|
|
FORMULA
|
G.f.: Product_{k>=2} 1/(1 + x^k).
a(n) ~ (-1)^n * Pi * exp(Pi*sqrt(n/6)) / (2^(13/4) * 3^(3/4) * n^(5/4)). - Vaclav Kotesovec, Jun 06 2018
|
|
MATHEMATICA
|
nmax = 78; CoefficientList[Series[Product[1/(1 + x^k), {k, 2, nmax}], {x, 0, nmax}], x]
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|