A010833 Expansion of Product_{k>=1} (1-x^k)^28.

1, -28, 350, -2520, 11025, -26180, 4158, 184600, -554400, 401100, 1496964, -3920280, 1444625, 6224400, -4972350, -7121296, -8308965, 50796900, -8971200, -121968000, 94011435, 80598288, 20282500, -175228200

Offset

0,2

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

Formula

a(0) = 1, a(n) = -(28/n) * Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - Seiichi Manyama, Aug 13 2023

Empirical: Sum_{n>=0} a(n) / exp(n*Pi) = (1/2048) * exp(7*Pi/6) * Pi^7 * sqrt(2) / Gamma(3/4)^28 = A388228. - Simon Plouffe, Sep 15 2025

Example

1 - 28*x + 350*x^2 - 2520*x^3 + 11025*x^4 - 26180*x^5 + 4158*x^6 + 184600*x^7 + ...

Crossrefs

Column k=28 of A286354.

Cf. A000203, A126581.

Sequence in context: A134288 A200968 A285739 * A022720 A272174 A173421

Adjacent sequences: A010830 A010831 A010832 * A010834 A010835 A010836

Keyword

sign,changed

Author

N. J. A. Sloane

Status

approved