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A306936
Coefficients of q-expansion of Eisenstein series G_{9/2}(tau) multiplied by 240.
2
1, 2, 0, 0, 242, 480, 0, 0, 2640, 4322, 0, 0, 11040, 13920, 0, 0, 30962, 39360, 0, 0, 65760, 73920, 0, 0, 125280, 156002, 0, 0, 216960, 226080, 0, 0, 340560, 406080, 0, 0, 522962, 541920, 0, 0, 756960, 860160, 0, 0, 1033440, 1063200, 0, 0, 1424160, 1646402, 0, 0, 1907040, 1860000, 0, 0
OFFSET
0,2
LINKS
X. Wang and D. Pei, Modular Forms with Integral and Half-Integral Weights, Science Press Beijing, Springer Berlin Heidelberg, 2012. x+432 pp.
D. Zagier, Modular Forms of One Variable, Notes based on a course given in Utrecht, 1991. See page 50.
PROG
(Sage)
def a(n):
if n==0: return 1
if (n%4) not in [0, 1]: return 0
D = Integer(n).squarefree_part()
f = Integer(sqrt(n/D))
if (D%4) not in [0, 1]: D, f = 4*D, f//2
X = kronecker_character(D)
s = sum([moebius(d)*X(d)*d^3*sigma(f/d, 7) for d in f.divisors()])
return round((240*X.lfunction(100)(-3)*s).real()) # Robin Visser, Feb 24 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Mar 16 2019
EXTENSIONS
More terms from Robin Visser, Feb 24 2024
STATUS
approved