A010821 Expansion of Product_{k>=1} (1 - x^k)^14.

1, -14, 77, -182, 0, 924, -1547, -506, 3003, 0, -1729, -8372, 9177, 13090, -15625, 0, -17017, 10556, 30107, 0, 7084, -89206, 11571, 69160, 0, 27132, 0, -19096, -153502, 0, 93093, 165242, 0, -38962, 0, -420838, 257439

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign

Examples

			1 - 14*x + 77*x^2 - 182*x^3 + 924*x^5 - 1547*x^6 - 506*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.
• S. R. Finch, Powers of Euler's q-Series, arXiv:math/0701251 [math.NT], 2007.
• Index entries for expansions of Product_{k >= 1} (1-x^k)^m

Programs

Mathematica

CoefficientList[Series[Product[(1-x^k)^14,{k,40}],{x,0,40}],x] (* Harvey P. Dale, Sep 03 2022 *)

Formula

a(0) = 1, a(n) = -(14/n)*Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - Seiichi Manyama, Mar 27 2017

G.f.: exp(-14*Sum_{k>=1} x^k/(k*(1 - x^k))). - Ilya Gutkovskiy, Feb 05 2018