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A010839 Expansion of Product_{k >= 1} (1-x^k)^48. 2
1, -48, 1080, -15040, 143820, -985824, 4857920, -16295040, 28412910, 38671600, -424520544, 1268350272, -1211937160, -4306546080, 18293091840, -23522231424, -26299018683, 137218594320, -150999182320, -134713340160 (list; graph; refs; listen; history; text; internal format)
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

Let b(q) be the determinant of the 3 X 3 Hankel matrix [E_4, E_6, E_8 ; E_6, E_8, E_10 ; E_8, E_10, E_12]. G.f. is -691*b(q)/(q^2*1728^2*250). - Seiichi Manyama, Jul 17 2017

a(n) = (A290010(n+2) - A290009(n+2) + 691*(A282330(n+2) - A282332(n+2)))/(1728^2*250). - Seiichi Manyama, Jul 19 2017

EXAMPLE

1 - 48*x + 1080*x^2 - 15040*x^3 + 143820*x^4 - 985824*x^5 + 4857920*x^6 - 16295040*x^7 + ...

CROSSREFS

Cf. A126581, A282330 (E_8^3), A282332 (E_6*E_8*E_10 = E4*E_10^2), A290009, A290010.

Sequence in context: A272778 A160068 A229387 * A000156 A319309 A022077

Adjacent sequences:  A010836 A010837 A010838 * A010840 A010841 A010842

KEYWORD

sign

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified October 19 20:37 EDT 2021. Contains 348091 sequences. (Running on oeis4.)