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%I #22 Aug 13 2023 08:47:27
%S 1,-30,405,-3190,15660,-45036,40745,222750,-974835,1334580,1547469,
%T -8174520,8380245,9200250,-23243355,-2643380,14704740,82050570,
%U -116275500,-195804810,442809990,25147930,-371898000,-313802910,125394405,1688931000,-1364323095,-737497840,158838945,-1653918750,6309965146,-1076120370
%N Expansion of Product_{k>=1} (1-x^k)^30.
%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="/A010835/b010835.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) = -(30/n) * Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - _Seiichi Manyama_, Aug 13 2023
%o (PARI) N=66; x='x+O('x^N); /* that many terms */
%o gf=eta(x)^30;
%o Vec(gf) /* show terms */ /* _Joerg Arndt_, Jul 30 2011 */
%Y Column k=30 of A286354.
%Y Cf. A000203, A082556.
%K sign
%O 0,2
%A _N. J. A. Sloane_
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