|
|
A004416
|
|
Expansion of (Sum_{n=-inf..inf} x^(n^2))^(-15).
|
|
1
|
|
|
1, -30, 480, -5440, 48930, -371136, 2464320, -14688000, 80001120, -403533790, 1904433984, -8477603520, 35829727680, -144548556480, 559157308800, -2081866609920, 7484792950050, -26057409056640, 88057506412320
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
a(n) ~ (-1)^n * exp(Pi*sqrt(m*n)) * m^((m+1)/4) / (2^(3*(m+1)/2) * n^((m+3)/4)), set m = 15 for this sequence. - Vaclav Kotesovec, Aug 18 2015
G.f.: 1/theta_3(x)^15, where theta_3() is the Jacobi theta function.
G.f.: Product_{k>=1} 1/((1 - x^(2*k))*(1 + x^(2*k-1))^2)^15. (End)
|
|
MATHEMATICA
|
nmax = 30; CoefficientList[Series[Product[((1 + (-x)^k)/(1 - (-x)^k))^15, {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 18 2015 *)
|
|
PROG
|
(PARI) q='q+O('q^99); Vec(((eta(q)*eta(q^4))^2/eta(q^2)^5)^15) \\ Altug Alkan, Sep 20 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|