A010837 Expansion of Product_{k>=1} (1-x^k)^32.

1, -32, 464, -3968, 21576, -72384, 109120, 215296, -1542684, 3135712, 217248, -14153856, 25215616, 2704192, -60182656, 43083520, 52111434, 50631680, -328746320, -68928128, 1172526144, -825260672, -1202344640

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=32 of A286354.

Cf. A000203, A082557.

Formula

a(0) = 1, a(n) = -(32/n) * Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - Seiichi Manyama, Aug 13 2023