A010825 Expansion of Product_{k>=1} (1 - x^k)^19.

1, -19, 152, -627, 1140, 988, -9063, 14212, 7410, -44270, 22781, 38114, 36176, -137256, -154850, 480605, -46493, -316065, -153406, -254525, 1156948, -184927, 88483, -1051042, -2381650, 3838874, 1417039, -542146

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) = -(19/n)*Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - Seiichi Manyama, Mar 27 2017

G.f.: exp(-19*Sum_{k>=1} x^k/(k*(1 - x^k))). - Ilya Gutkovskiy, Feb 05 2018