A010841 Expansion of Product_{k>=1} (1-x^k)^64.

1, -64, 1952, -37632, 512400, -5207936, 40618368, -244952576, 1124362248, -3684692800, 6607738816, 8603838208, -109557823168, 389162471040, -599467398400, -815811136000, 6834665221028, -15689583552384, 5284986829472, 66706108652800, -183175485196256, 124242038746624

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.
• Index entries for expansions of Product_{k >= 1} (1-x^k)^m

Crossrefs

Column k=64 of A286354.

Cf. A000203, A082559.

Programs

Mathematica

nmax=20; CoefficientList[Series[Product[(1-x^k)^64,{k,nmax}],{x,0,nmax}],x] (* Stefano Spezia, May 27 2025 *)

Formula

a(0) = 1, a(n) = -(64/n) * Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - Seiichi Manyama, Aug 13 2023