OFFSET
1,2
COMMENTS
That is, a(n) = J_1(k) where k is the n-th number >= -1 which is == -1 or 0 mod 4.
REFERENCES
M. Kaneko, The Fourier coefficients and the singular moduli of the elliptic modular function j(tau), Memoirs Faculty Engin. Sci., Kyoto Inst. Technology, 44 (March 1996), pp. 1-5.
M. Kaneko, Fourier coefficients of the elliptic modular function j(tau) (in Japanese), Rokko Lectures in Mathematics 10, Dept. Math., Faculty of Science, Kobe University, Rokko, Kobe, Japan, 2001.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..10000 (terms 1..1002 from N. J. A. Sloane)
D. Zagier, Traces of singular moduli
FORMULA
For recurrence see Maple code.
a(n) ~ (-1)^n * exp(Pi*sqrt(2*n)). - Vaclav Kotesovec, Oct 06 2019
MAPLE
with(numtheory); M:=30; t[ -1]:=-1; t[0]:=2;
for n from 1 to M do
t[4*n-1]:=-240*sigma[3](n)-add( r^2*t[4*n-r^2], r=2..floor(sqrt(4*n+1)));
t[4*n]:=-2*add( t[4*n-r^2], r=1..floor(sqrt(4*n+1)));
lprint(t[4*n-1], t[4*n]); od:
CROSSREFS
KEYWORD
sign
AUTHOR
EXTENSIONS
Entry revised by N. J. A. Sloane, Jul 24 2006
STATUS
approved