OFFSET
1,2
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..200
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_5 j^_1 in terms of powers of j^-1 is given by T_5 j^-1 = 49336682190*j^-1 - 122566701099729715200000*j^-2 + 177278377115100363578123747328000000*j^-3 - ....
The first coefficient factors as 49336682190 = 2 * 3 * 5 * 1644556073, so a(1) = 1.
The second coefficient factors as -122566701099729715200000 = -2^18 * 3^4 * 5^5 * 1847130309301, so a(2) = 18.
The third coefficient factors as 177278377115100363578123747328000000 = 2^33 * 3^7 * 5^6 * 31 * 47 * 414512421715739, so a(3) = 33. (End)
PROG
(Sage)
def a(n):
j1 = sum([1]+[240*sigma(k, 3)*x^k for k in range(1, 5*n)])
j2 = product([x]+[(1-x^k)^24 for k in range(1, 5*n)])
jinv = (j2/j1^3).taylor(x, 0, 5*n)
T5jinv = sum([jinv.coefficient(x^(5*k))*x^k for k in range(n+1)]+
[jinv.coefficient(x^k)*x^(5*k)/5 for k in range(n)])
for k in range(1, n):
c = T5jinv.taylor(x, 0, k).coefficient(x^k)
T5jinv -= c*(jinv^k)
coeff = T5jinv.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