0,2

Expansion of b(q^2)^2 / b(-q) in powers of q where b() is a cubic AGM function.

Expansion of eta(q)^3 * eta(q^4)^3 * eta(q^6) / ( eta(q^2)^3 * eta(q^3) * eta(q^12) ) in powers of q.

Euler transform of period 12 sequence [ -3, 0, -2, -3, -3, 0, -3, -3, -2, 0, -3, -2, ...].

Moebius transform is period 12 sequence [ -3, 6, 0, 0, 3, 0, -3, 0, 0, -6, 3, 0, ...].

G.f. is a period 1 Fourier series which satisfies f(-1 / (12 t)) = 108^(1/2) (t/i) g(t) where q = exp(2 pi i t) and g(t) is g.f. for A113447.

a(6*n+5) = 0.

G.f.: Product_{k>0} (1 - x^k)^3 * (1 + x^(2*k))^3 / ((1 - x^(3*k)) * (1 + x^(6*k))).

G.f.: 1 + 3 * Sum_{k>0} (-1)^k * (x^k + x^(3*k)) / (1 + x^k + x^(2*k)).

G.f.: 1 + 3 * ( Sum_{k>0} x^(6*k-5) / ( 1 + x^(6*k-5) ) - x^(6*k-1) / ( 1 + x^(6*k-1) )).

1 - 3*q + 3*q^2 - 3*q^3 + 3*q^4 + 3*q^6 - 6*q^7 + 3*q^8 - 3*q^9 + 3*q^12 + ...

(PARI) {a(n) = if( n<1, n==0, 3 * (-1)^n * sumdiv(n, d, kronecker(-12, d)))}

(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A)^3 * eta(x^4 + A)^3 * eta(x^6 + A) / ( eta(x^2 + A)^3 * eta(x^3 + A) * eta(x^12 + A ) ), n))}

(-1)^n * A107760(n) = a(n). Convolution inverse of A132974.

Sequence in context: A031354 A033700 A122916 this_sequence A107760 A138070 A081334

Adjacent sequences: A132970 A132971 A132972 this_sequence A132974 A132975 A132976

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Michael Somos, Sep 07 2007