A010821 - OEIS

%I #26 Sep 03 2022 19:46:19

%S 1,-14,77,-182,0,924,-1547,-506,3003,0,-1729,-8372,9177,13090,-15625,

%T 0,-17017,10556,30107,0,7084,-89206,11571,69160,0,27132,0,-19096,

%U -153502,0,93093,165242,0,-38962,0,-420838,257439

%N Expansion of Product_{k>=1} (1 - x^k)^14.

%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="/A010821/b010821.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 S. R. Finch, <a href="http://arXiv.org/abs/math.NT/0701251">Powers of Euler's q-Series</a>, arXiv:math/0701251 [math.NT], 2007.

%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) = -(14/n)*Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - _Seiichi Manyama_, Mar 27 2017

%F G.f.: exp(-14*Sum_{k>=1} x^k/(k*(1 - x^k))). - _Ilya Gutkovskiy_, Feb 05 2018

%e 1 - 14*x + 77*x^2 - 182*x^3 + 924*x^5 - 1547*x^6 - 506*x^7 + ...

%t CoefficientList[Series[Product[(1-x^k)^14,{k,40}],{x,0,40}],x] (* _Harvey P. Dale_, Sep 03 2022 *)

%K sign

%O 0,2

%A _N. J. A. Sloane_.