A010836 Expansion of Product_{k>=1} (1-x^k)^31.

1, -31, 434, -3565, 18445, -57505, 70091, 227447, -1241550, 2102730, 1139498, -11000164, 15185009, 8060465, -39266925, 11975548, 33735905, 79961555, -212042635, -176681400, 762467041, -231771190, -762218948, -59474275, 687626655, 2193123086, -3317871844

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=31 of A286354.

Cf. A000203.

Formula

a(0) = 1, a(n) = -(31/n) * Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - Seiichi Manyama, Aug 13 2023