A010840 Expansion of Product_{k>=1} (1-x^k)^40.

1, -40, 740, -8320, 62530, -322048, 1085240, -1799680, -2821065, 26012480, -66837420, 35093760, 268749870, -783902720, 526221400, 1691816960, -3960854625, 1042577120, 5103133240, -380798080, -10159511430

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=40 of A286354.

Cf. A000203.

Formula

a(0) = 1, a(n) = -(40/n) * Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - Seiichi Manyama, Aug 13 2023