A010831 Expansion of Product_{k>=1} (1-x^k)^26.

1, -26, 299, -1950, 7475, -13754, -12220, 132756, -276575, 0, 1010100, -1486030, -519961, 2486300, 829725, -2215486, -11643060, 18523050, 16317925, -42861650, 0, 11010090, 59644221, -5743400, -138219900

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign

Examples

			1 - 26*x + 299*x^2 - 1950*x^3 + 7475*x^4 - 13754*x^5 - 12220*x^6 + 132756*x^7 + ...
		

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.
• S. R. Finch, Powers of Euler's q-Series, arXiv:math/0701251 [math.NT], 2007.
• Index entries for expansions of Product_{k >= 1} (1-x^k)^m

Crossrefs

Column k=26 of A286354.

Cf. A000203, A126581, A322433.

Programs

Mathematica

CoefficientList[Expand@ Product[(1 - x^k)^26, {k, 25}], x, 25] (* Michael De Vlieger, Jun 08 2016 *)

Formula

a(0) = 1, a(n) = -(26/n) * Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - Seiichi Manyama, Aug 13 2023