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
Expansion of q^(-11/24) * eta(q)^11 in powers of q. - Michael Somos, May 28 2013
a(n) == A010815(n) (mod 11). - Michael Somos, May 28 2013
a(0) = 1, a(n) = -(11/n)*Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - Seiichi Manyama, Mar 27 2017
G.f.: exp(-11*Sum_{k>=1} x^k/(k*(1 - x^k))). - Ilya Gutkovskiy, Feb 05 2018
EXAMPLE
1 - 11*x + 44*x^2 - 55*x^3 - 110*x^4 + 374*x^5 - 143*x^6 - 462*x^7 + ...
q^11 - 11*q^35 + 44*q^59 - 55*q^83 - 110*q^107 + 374*q^131 - 143*q^155 + ...
MATHEMATICA
a[ n_] := SeriesCoefficient[ QPochhammer[ q]^11, {q, 0, n}] (* Michael Somos, May 28 2013 *)
a[ n_] := SeriesCoefficient[ Product[ 1 - q^k, {k, n}]^11, {q, 0, n}] (* Michael Somos, May 28 2013 *)
PROG
(PARI) {a(n) = if( n<0, 0, polcoeff( eta(x + x * O(x^n))^11, n))} /* Michael Somos, May 28 2013 */
CROSSREFS
KEYWORD
sign
AUTHOR
STATUS
approved