A010817 - OEIS

%I #27 Mar 10 2018 11:01:52

%S 1,-9,27,-12,-90,135,54,-99,-189,-85,657,-162,-135,-171,-810,702,495,

%T 837,-673,-900,243,-1053,-297,1566,2700,-1764,81,-1188,-1377,270,

%U -2043,3321,-756,3726,3015,-4563,-3348,504,-351,-1350,-468

%N Expansion of Product_{k>=1} (1 - x^k)^9.

%D 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.

%H Seiichi Manyama, <a href="/A010817/b010817.txt">Table of n, a(n) for n = 0..10000</a>

%H M. Boylan, <a href="http://dx.doi.org/10.1016/S0022-314X(02)00037-9">Exceptional congruences for the coefficients of certain eta-product newforms</a>, J. Number Theory 98 (2003), no. 2, 377-389. MR1955423 (2003k:11071)

%H M. Newman, <a href="/A000727/a000727.pdf">A table of the coefficients of the powers of eta(tau)</a>, Nederl. Akad. Wetensch. Proc. Ser. A. 59 = Indag. Math. 18 (1956), 204-216. [Annotated scanned copy]

%H <a href="/index/Pro#1mxtok">Index entries for expansions of Product_{k >= 1} (1-x^k)^m</a>

%F a(0) = 1, a(n) = -(9/n)*Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - _Seiichi Manyama_, Mar 27 2017

%F G.f.: exp(-9*Sum_{k>=1} x^k/(k*(1 - x^k))). - _Ilya Gutkovskiy_, Feb 05 2018

%F (Julia) # DedekindEta is defined in A000594.

%F A010817List(len) = DedekindEta(len, 9)

%F A010817List(41) |> println # _Peter Luschny_, Mar 10 2018

%K sign

%O 0,2

%A _N. J. A. Sloane_