A010826 Expansion of Product_{k>=1} (1 - x^k)^20.

1, -20, 170, -760, 1615, 476, -11210, 22440, 1615, -64600, 60002, 51680, -9520, -213180, -83980, 803528, -379525, -692360, 119700, 80920, 1899830, -1235360, -755990, -1200040, -1981435, 8388956, -361760, -5068440

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign

References

• 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.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000
• M. Boylan, Exceptional congruences for the coefficients of certain eta-product newforms, J. Number Theory 98 (2003), no. 2, 377-389.
• Index entries for expansions of Product_{k >= 1} (1-x^k)^m

Formula

a(0) = 1, a(n) = -(20/n)*Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - Seiichi Manyama, Mar 27 2017

G.f.: exp(-20*Sum_{k>=1} x^k/(k*(1 - x^k))). - Ilya Gutkovskiy, Feb 05 2018