A010824 Expansion of Product_{k>=1} (1 - x^k)^18.

1, -18, 135, -510, 765, 1242, -7038, 8280, 9180, -27710, 3519, 20196, 50370, -68850, -153765, 244782, 52785, -71010, -130525, -343620, 517293, 54978, 498780, -390150, -1835865, 1161270, 896751, 793730, -633420

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) = -(18/n)*Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - Seiichi Manyama, Mar 27 2017

G.f.: exp(-18*Sum_{k>=1} x^k/(k*(1 - x^k))). - Ilya Gutkovskiy, Feb 05 2018