A010823 Expansion of Product_{k>=1} (1 - x^k)^17.

1, -17, 119, -408, 476, 1309, -5236, 4233, 8602, -15470, -4250, 5236, 45815, -21182, -117776, 101065, 46767, 36685, -36771, -267036, 143514, -18241, 486285, 81753, -1007250, 104006, 165767, 579292, 78829, 187510

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

Programs

Mathematica

With[{nn=50},CoefficientList[Series[Product[(1-x^k)^17,{k,nn}],{x,0,nn}],x]] (* Harvey P. Dale, Jul 24 2019 *)

Formula

a(0) = 1, a(n) = -(17/n)*Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - Seiichi Manyama, Mar 27 2017

G.f.: exp(-17*Sum_{k>=1} x^k/(k*(1 - x^k))). - Ilya Gutkovskiy, Feb 05 2018