OFFSET
0,2
REFERENCES
Newman, Morris; A table of the coefficients of the powers of eta(tau). Nederl. Akad. Wetensch. Proc. Ser. A. 59 = Indag. Math. 18 (1956), 204-216.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..10000
M. Boylan, Exceptional congruences for the coefficients of certain eta-product newforms, J. Number Theory 98 (2003), no. 2, 377-389.
FORMULA
a(0) = 1, a(n) = -(64/n) * Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - Seiichi Manyama, Aug 13 2023
Empirical: Sum_{n>=0} a(n) / exp(n*Pi) = (1/16777216) * exp(8*Pi/3) * Pi^16 / Gamma(3/4)^64 = A388236. - Simon Plouffe, Sep 15 2025
MATHEMATICA
nmax=20; CoefficientList[Series[Product[(1-x^k)^64, {k, nmax}], {x, 0, nmax}], x] (* Stefano Spezia, May 27 2025 *)
CROSSREFS
KEYWORD
sign
AUTHOR
STATUS
approved
