A010835 Expansion of Product_{k>=1} (1-x^k)^30.

1, -30, 405, -3190, 15660, -45036, 40745, 222750, -974835, 1334580, 1547469, -8174520, 8380245, 9200250, -23243355, -2643380, 14704740, 82050570, -116275500, -195804810, 442809990, 25147930, -371898000, -313802910, 125394405, 1688931000, -1364323095, -737497840, 158838945, -1653918750, 6309965146, -1076120370

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=30 of A286354.

Cf. A000203, A082556.

Programs

PARI

N=66; x='x+O('x^N); /* that many terms */
gf=eta(x)^30;
Vec(gf)  /* show terms */ /* Joerg Arndt, Jul 30 2011 */

Formula

a(0) = 1, a(n) = -(30/n) * Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - Seiichi Manyama, Aug 13 2023