A010830 Expansion of Product_{k>=1} (1-x^k)^25.

1, -25, 275, -1700, 6050, -9405, -15550, 107525, -182875, -81675, 756655, -801550, -662975, 1220175, 1361350, -209440, -9601900, 8608900, 14889050, -19948500, -6262465, -7057550, 38788925, 19716425, -69119875, 23579969, -82427400, 98068850, 191984400

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

Crossrefs

Column k=25 of A286354.

Cf. A000203.

Formula

a(0) = 1, a(n) = -(25/n) * Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - Seiichi Manyama, Aug 13 2023