%I #21 Aug 13 2023 08:47:34
%S 1,-44,902,-11352,96965,-582692,2428382,-6245448,3684670,43828180,
%T -195750104,340202584,211248851,-2418539816,4734800950,-43313600,
%U -16560186918,26632794760,4021681554,-50231748600,12519655368
%N Expansion of Product_{k>=1} (1-x^k)^44.
%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="/A010838/b010838.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) = -(44/n) * Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - _Seiichi Manyama_, Aug 13 2023
%t With[{nn=20},CoefficientList[Series[Product[(1-x^k)^44,{k,nn}],{x,0,nn}],x]] (* _Harvey P. Dale_, Mar 23 2015 *)
%Y Column k=44 of A286354.
%Y Cf. A000203.
%K sign
%O 0,2
%A _N. J. A. Sloane_