A010820 Expansion of Product_{k>=1} (1 - x^k)^13.

1, -13, 65, -130, -65, 728, -871, -715, 1560, 845, 78, -6513, 2730, 8605, -4355, 2483, -13299, -2275, 11440, 10010, 19734, -41834, -11375, 12870, -2730, 14911, 33201, 25155, -70070, -36595, -28925, 64389, 13650, 52780

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign

Examples

			1 - 13*x + 65*x^2 - 130*x^3 - 65*x^4 + 728*x^5 - 871*x^6 - 715*x^7 + ...
		

References

• 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.

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) = -(13/n)*Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - Seiichi Manyama, Mar 27 2017

G.f.: exp(-13*Sum_{k>=1} x^k/(k*(1 - x^k))). - Ilya Gutkovskiy, Feb 05 2018