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Expansion of Product_{k>=1} (1-x^k)^40.
6

%I #20 Aug 13 2023 08:47:41

%S 1,-40,740,-8320,62530,-322048,1085240,-1799680,-2821065,26012480,

%T -66837420,35093760,268749870,-783902720,526221400,1691816960,

%U -3960854625,1042577120,5103133240,-380798080,-10159511430

%N Expansion of Product_{k>=1} (1-x^k)^40.

%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="/A010840/b010840.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) = -(40/n) * Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - _Seiichi Manyama_, Aug 13 2023

%Y Column k=40 of A286354.

%Y Cf. A000203.

%K sign

%O 0,2

%A _N. J. A. Sloane_