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A010820

Expansion of Product_{k>=1} (1 - x^k)^13.

1, -13, 65, -130, -65, 728, -871, -715, 1560, 845, 78, -6513, 2730, 8605, -4355, 2483, -13299, -2275, 11440, 10010, 19734, -41834, -11375, 12870, -2730, 14911, 33201, 25155, -70070, -36595, -28925, 64389, 13650, 52780

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OFFSET

0,2

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

FORMULA

a(0) = 1, a(n) = -(13/n)*Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - Seiichi Manyama, Mar 27 2017

G.f.: exp(-13*Sum_{k>=1} x^k/(k*(1 - x^k))). - Ilya Gutkovskiy, Feb 05 2018

Empirical: Sum_{n>=0} a(n) / exp(n*Pi) = (1/32) * exp(13*Pi/24) * Pi^(13/4) * 2^(1/8) / Gamma(3/4)^13 = A388215. - Simon Plouffe, Sep 15 2025

EXAMPLE

1 - 13*x + 65*x^2 - 130*x^3 - 65*x^4 + 728*x^5 - 871*x^6 - 715*x^7 + ...

CROSSREFS

Sequence in context: A302425 A303195 A283169 * A022705 A153793 A067160

Adjacent sequences: A010817 A010818 A010819 * A010821 A010822 A010823

KEYWORD

sign

AUTHOR

N. J. A. Sloane

STATUS

approved

URL: https://oeis.org/A010820

⇱ A010820 - OEIS