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Expansion of Product_{k>=1} (1-x^k)^28.
1

%I #24 Aug 13 2023 08:47:19

%S 1,-28,350,-2520,11025,-26180,4158,184600,-554400,401100,1496964,

%T -3920280,1444625,6224400,-4972350,-7121296,-8308965,50796900,

%U -8971200,-121968000,94011435,80598288,20282500,-175228200

%N Expansion of Product_{k>=1} (1-x^k)^28.

%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="/A010833/b010833.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) = -(28/n) * Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - _Seiichi Manyama_, Aug 13 2023

%e 1 - 28*x + 350*x^2 - 2520*x^3 + 11025*x^4 - 26180*x^5 + 4158*x^6 + 184600*x^7 + ...

%Y Column k=28 of A286354.

%Y Cf. A000203, A126581.

%K sign

%O 0,2

%A _N. J. A. Sloane_