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A276491
Expansion of q*Product_{k>=1} (1-q^(2*k))^2*(1-q^(10*k))^2.
2
1, 0, -2, 0, -1, 0, 2, 0, 1, 0, 0, 0, 2, 0, 2, 0, -6, 0, -4, 0, -4, 0, 6, 0, 1, 0, 4, 0, 6, 0, -4, 0, 0, 0, -2, 0, 2, 0, -4, 0, 6, 0, -10, 0, -1, 0, -6, 0, -3, 0, 12, 0, -6, 0, 0, 0, 8, 0, 12, 0, 2, 0, 2, 0, -2, 0, 2, 0, -12, 0, -12, 0, 2, 0, -2, 0, 0, 0, 8, 0, -11, 0, 6, 0, 6, 0, -12, 0, -6, 0, 4, 0, 8, 0, 4, 0, 2, 0, 0, 0, 6, 0, 14, 0, 4, 0, -6, 0, 2, 0, -4, 0, -6, 0, -6, 0, 2, 0, -12, 0, -11, 0, -12, 0, -1, 0, 2, 0, 20, 0, 0, 0, -8, 0, -4
OFFSET
1,3
COMMENTS
Multiplicative. See A030205 for formula. - Andrew Howroyd, Aug 05 2018
LINKS
Yves Martin and Ken Ono, Eta-Quotients and Elliptic Curves, Proc. Amer. Math. Soc. 125, No 11 (1997), 3169-3176.
FORMULA
a(2n-1) = A030205(n-1), a(2n) = 0 for n > 0.
G.f.: (eta(x^2) * eta(x^10))^2. - Andrew Howroyd, Aug 05 2018
Euler transform of period 10 sequence [0, -2, 0, -2, 0, -2, 0, -2, 0, -4, ...]. - Georg Fischer, Nov 17 2022
MATHEMATICA
QPochhammer[x^2]^2*QPochhammer[x^10]^2 + O[x]^100 // CoefficientList[#, x]& (* Jean-François Alcover, Sep 19 2019 *)
PROG
(PARI) seq(n)={Vec((eta(x^2 + O(x*x^n)) * eta(x^10 + O(x*x^n)))^2)} \\ Andrew Howroyd, Aug 05 2018
CROSSREFS
KEYWORD
sign,mult
AUTHOR
Seiichi Manyama, Sep 10 2016
STATUS
approved