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%I M3742 N1529 #38 Feb 01 2022 01:10:53
%S 1,-5,5,10,-15,-6,-5,25,15,-20,9,-45,-5,25,20,10,15,20,-50,-35,-30,55,
%T -50,15,80,1,50,-35,-45,-15,5,-50,-25,-55,85,51,50,10,-40,65,10,-10,
%U -115,50,-115,-100,85,80,-30,5,20,45,70,65,45,-55,-100
%N Expansion of Product_{n>=1} (1-x^n)^5.
%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.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Seiichi Manyama, <a href="/A000728/b000728.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) = -(5/n)*Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - _Seiichi Manyama_, Mar 26 2017
%F G.f.: exp(-5*Sum_{k>=1} x^k/(k*(1 - x^k))). - _Ilya Gutkovskiy_, Feb 05 2018
%t CoefficientList[QPochhammer[x]^5 + O[x]^60, x] (* _Jean-François Alcover_, Feb 10 2016 *)
%Y Cf. A258405.
%K sign
%O 0,2
%A _N. J. A. Sloane_
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