A131797 Expansion of eta(q) * eta(q^15) / (eta(q^6) * eta(q^10)) in powers of q.

1, -1, -1, 0, 0, 1, 1, 0, -1, 0, 1, 0, 0, -1, -2, -1, 2, 3, 1, -1, -2, -3, 0, 3, 1, -2, -2, 0, 2, 6, 3, -4, -7, -3, 2, 5, 6, -2, -8, -3, 5, 6, 2, -4, -12, -7, 10, 15, 6, -5, -13, -12, 4, 18, 7, -11, -14, -6, 10, 24, 14, -20, -32, -12, 12, 29, 24, -9, -36, -15

Offset

0,15

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Formula

Euler transform of period 30 sequence [ -1, -1, -1, -1, -1, 0, -1, -1, -1, 0, -1, 0, -1, -1, -2, -1, -1, 0, -1, 0, -1, -1, -1, 0, -1, -1, -1, -1, -1, 0, ...].

G.f. A(x) satisfies 0 = f(A(x), A(x^2)) where f(u, v) = v*(u^2 - v) - 2 * u * (u-1).

G.f. is a period 1 Fourier series which satisfies f(-1 / (30 t)) = 2 * g(t) where q = exp(2 Pi i t) and g() is the g.f. for A094022.

G.f.: Product_{k>0} (1 - x^k) * (1 - x^(15*k)) / ((1 - x^(6*k)) * (1 - x^(10*k))).

a(n) = -A131794(n) = -A131796(n) unless n=0.

Convolution inverse of A094023.

a(n) = (-1)^n * A145727(n). - Michael Somos, Nov 11 2015

Example

G.f. = 1 - q - q^2 + q^5 + q^6 - q^8 + q^10 - q^13 - 2*q^14 - q^15 + 2*q^16 + ...

Mathematica

a[ n_] := SeriesCoefficient[ QPochhammer[ q] QPochhammer[ q^15] / (QPochhammer[ q^6] QPochhammer[ q^10]), {q, 0, n}]; (* Michael Somos, Aug 26 2015 *)

Prog

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A) * eta(x^15 + A) / (eta(x^6 + A) * eta(x^10 + A)), n))};

Crossrefs

Cf. A094022, A094023, A131794, A131796, A145727.

Sequence in context: A294859 A336320 A145782 * A145727 A131796 A131794

Adjacent sequences: A131794 A131795 A131796 * A131798 A131799 A131800

Keyword

sign

Author

Michael Somos, Jul 16 2007

Status

approved