OFFSET
1,1
COMMENTS
Jan Vonk observed that a(n) ~ 15*n. - Robin Visser, Jul 30 2023
LINKS
Robin Visser, Table of n, a(n) for n = 1..250
Jan Vonk, Overconvergent modular forms and their explicit arithmetic, Bulletin of the American Mathematical Society 58.3 (2021): 313-356.
EXAMPLE
From Robin Visser, Jul 30 2023: (Start)
An expansion for T_3 j^_1 in terms of powers of j^-1 is given by T_3 j^-1 = 356652*j^-1 - 16114360320000*j^-2 + 1298216343568384000000/3*j^-3 - ....
The first coefficient factors as 356652 = 2^2 * 3^2 * 9907, so a(1) = 2.
The second coefficient factors as -16114360320000 = -2^16 * 3^5 * 5^4 * 1619, so a(2) = 16.
The third coefficient factors as 1298216343568384000000/3 = 2^32 * 3^-1 * 5^6 * 19344931, so a(3) = 32. (End)
PROG
(Sage)
def a(n):
j1 = sum([1]+[240*sigma(k, 3)*x^k for k in range(1, 3*n)])
j2 = product([x]+[(1-x^k)^24 for k in range(1, 3*n)])
jinv = (j2/j1^3).taylor(x, 0, 3*n)
T3jinv = sum([jinv.coefficient(x^(3*k))*x^k for k in range(n+1)]+
[jinv.coefficient(x^k)*x^(3*k)/3 for k in range(n)])
for k in range(1, n):
c = T3jinv.taylor(x, 0, k).coefficient(x^k)
T3jinv -= c*(jinv^k)
coeff = T3jinv.taylor(x, 0, n).coefficient(x^n)
return Rational(coeff).valuation(2) # Robin Visser, Jul 30 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jun 17 2021
EXTENSIONS
More terms from Robin Visser, Jul 30 2023
STATUS
approved