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Expansion of Product_{k>=1} (1 - x^k)^17.
2

%I #20 Jul 24 2019 19:16:20

%S 1,-17,119,-408,476,1309,-5236,4233,8602,-15470,-4250,5236,45815,

%T -21182,-117776,101065,46767,36685,-36771,-267036,143514,-18241,

%U 486285,81753,-1007250,104006,165767,579292,78829,187510

%N Expansion of Product_{k>=1} (1 - x^k)^17.

%D Morris Newman, 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="/A010823/b010823.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.

%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) = -(17/n)*Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - _Seiichi Manyama_, Mar 27 2017

%F G.f.: exp(-17*Sum_{k>=1} x^k/(k*(1 - x^k))). - _Ilya Gutkovskiy_, Feb 05 2018

%t With[{nn=50},CoefficientList[Series[Product[(1-x^k)^17,{k,nn}],{x,0,nn}],x]] (* _Harvey P. Dale_, Jul 24 2019 *)

%K sign

%O 0,2

%A _N. J. A. Sloane_.