A276491 Expansion of q*Product_{k>=1} (1-q^(2*k))^2*(1-q^(10*k))^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

Author

Seiichi Manyama, Sep 10 2016

Keywords

• sign
• mult

Comments

Multiplicative. See A030205 for formula. - Andrew Howroyd, Aug 05 2018

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..1000
• Yves Martin and Ken Ono, Eta-Quotients and Elliptic Curves, Proc. Amer. Math. Soc. 125, No 11 (1997), 3169-3176.

Crossrefs

Cf. A030205, A272207, A276030.

Programs

Mathematica

QPochhammer[x^2]^2*QPochhammer[x^10]^2 + O[x]^100 // CoefficientList[#, x]& (* Jean-François Alcover, Sep 19 2019 *)

PARI

seq(n)={Vec((eta(x^2 + O(x*x^n)) * eta(x^10 + O(x*x^n)))^2)} \\ Andrew Howroyd, Aug 05 2018

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