A010829 Expansion of Product_{k>=1} (1 - x^k)^23.

1, -23, 230, -1265, 3795, -3519, -16445, 64285, -64515, -120175, 354706, -123763, -407560, -48530, 817190, 1464341, -4376693, -135355, 6303955, -1282710, -682088, -11372603, 5678585, 13479425, -5451115, 16579596

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) = -(23/n)*Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - Seiichi Manyama, Mar 27 2017

G.f.: exp(-23*Sum_{k>=1} x^k/(k*(1 - x^k))). - Ilya Gutkovskiy, Feb 05 2018

Empirical: Sum_{n>=0} a(n) / exp(n*Pi) = (1/512) * exp(23*Pi/24) * Pi^(23/4) * 2^(3/8) / Gamma(3/4)^23 = A388224. - Simon Plouffe, Sep 15 2025

Crossrefs

Sequence in context: A179631 A144248 A124336 * A022715 A060189 A028824

Adjacent sequences: A010826 A010827 A010828 * A010830 A010831 A010832

Keyword

sign

Author

N. J. A. Sloane

Status

approved