A010819 Expansion of Product_{k>=1} (1 - x^k)^11.

1, -11, 44, -55, -110, 374, -143, -462, 55, 495, 1287, -2069, -902, 1210, -275, 3795, -1507, -2431, -3575, -385, 8690, -1661, 1143, 1265, -4290, -12716, 2299, 11440, 3905, 8635, -10472, 6105, -20548, -1540, 8690, -24904, 29634, 25003, 8470, -23320, -18183

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign

Examples

			1 - 11*x + 44*x^2 - 55*x^3 - 110*x^4 + 374*x^5 - 143*x^6 - 462*x^7 + ...
q^11 - 11*q^35 + 44*q^59 - 55*q^83 - 110*q^107 + 374*q^131 - 143*q^155 + ...
		

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

Cf. A010815.

Programs

Mathematica

a[ n_] := SeriesCoefficient[ QPochhammer[ q]^11, {q, 0, n}] (* Michael Somos, May 28 2013 *)
a[ n_] := SeriesCoefficient[ Product[ 1 - q^k, {k, n}]^11, {q, 0, n}] (* Michael Somos, May 28 2013 *)

PARI

{a(n) = if( n<0, 0, polcoeff( eta(x + x * O(x^n))^11, n))} /* Michael Somos, May 28 2013 */

Formula

Expansion of q^(-11/24) * eta(q)^11 in powers of q. - Michael Somos, May 28 2013

a(n) == A010815(n) (mod 11). - Michael Somos, May 28 2013

a(0) = 1, a(n) = -(11/n)*Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - Seiichi Manyama, Mar 27 2017

G.f.: exp(-11*Sum_{k>=1} x^k/(k*(1 - x^k))). - Ilya Gutkovskiy, Feb 05 2018