|
|
A292520
|
|
Expansion of Product_{k>=1} 1/(1 + x^(k^2)).
|
|
7
|
|
|
1, -1, 1, -1, 0, 0, 0, 0, 1, -2, 2, -2, 1, 0, 0, 0, 0, -1, 2, -2, 2, -1, 0, 0, 0, -1, 2, -3, 3, -2, 1, 0, 1, -2, 3, -4, 3, -2, 1, 0, 1, -2, 3, -4, 3, -2, 1, 0, 0, -2, 4, -5, 6, -4, 2, -1, 0, -2, 5, -7, 8, -6, 3, -1, 0, -1, 3, -6, 7, -6, 4, -1, 1, -1, 3, -6, 7, -8, 6, -3, 2, -4, 6, -9, 11, -9, 7, -4, 1, -3, 7
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,10
|
|
COMMENTS
|
The difference between the number of partitions of n into an even number of squares and the number of partitions of n into an odd number of squares.
|
|
LINKS
|
|
|
FORMULA
|
G.f.: Product_{k>=1} 1/(1 + x^(k^2)).
a(n) ~ (-1)^n * exp(3 * Pi^(1/3) * Zeta(3/2)^(2/3) * n^(1/3) / 2^(7/3)) * Zeta(3/2)^(1/3) / (2^(5/3) * sqrt(3) * Pi^(1/3) * n^(5/6)). - Vaclav Kotesovec, Sep 19 2017
|
|
MATHEMATICA
|
nmax = 100; CoefficientList[Series[Product[1/(1 + x^(k^2)), {k, 1, Floor[Sqrt[nmax]] + 1}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 19 2017 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|