A010817 Expansion of Product_{k>=1} (1 - x^k)^9.

1, -9, 27, -12, -90, 135, 54, -99, -189, -85, 657, -162, -135, -171, -810, 702, 495, 837, -673, -900, 243, -1053, -297, 1566, 2700, -1764, 81, -1188, -1377, 270, -2043, 3321, -756, 3726, 3015, -4563, -3348, 504, -351, -1350, -468

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign

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. MR1955423 (2003k:11071)
• M. 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. [Annotated scanned copy]
• Index entries for expansions of Product_{k >= 1} (1-x^k)^m

Crossrefs

Cf. A000203.

Programs

Julia

# DedekindEta is defined in A000594.
A010817List(len) = DedekindEta(len, 9)
A010817List(41) |> println # Peter Luschny, Mar 10 2018

Formula

a(0) = 1, a(n) = -(9/n)*Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - Seiichi Manyama, Mar 27 2017

G.f.: exp(-9*Sum_{k>=1} x^k/(k*(1 - x^k))). - Ilya Gutkovskiy, Feb 05 2018