A147702 Expansion of eta(q) * eta(q^10)^3 / (eta(q^2) * eta(q^4) * eta(q^5) * eta(q^20)) in powers of q.

1, -1, 0, -1, 2, -1, 0, -2, 4, -3, 0, -3, 8, -4, 0, -6, 14, -8, 0, -10, 22, -12, 0, -16, 36, -21, 0, -25, 56, -30, 0, -38, 84, -48, 0, -57, 126, -68, 0, -84, 184, -102, 0, -121, 264, -143, 0, -172, 376, -207, 0, -243, 528, -284, 0, -338, 732, -400, 0, -465, 1008, -542, 0, -636, 1374, -744, 0, -862, 1856, -996, 0

Offset

0,5

Comments

Ramanujan theta functions: f(q) (see A121373), phi(q) (A000122), psi(q) (A010054), chi(q) (A000700).

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Michael Somos, Introduction to Ramanujan theta functions

Eric Weisstein's World of Mathematics, Ramanujan Theta Functions

Formula

Expansion of chi(-q) * f(q^5) / f(-q^4) in powers of q where f(), chi() are Ramanujan theta functions.

Euler transform of period 20 sequence [ -1, 0, -1, 1, 0, 0, -1, 1, -1, -2, -1, 1, -1, 0, 0, 1, -1, 0, -1, 0, ...].

G.f. is a period 1 Fourier series which satisfies f(-1 / (80 t)) = (5/4)^(-1/2) g(t) where q = exp(2 Pi i t) and g() is the g.f. for A147699.

a(2*n + 1) = - A036026(n). a(4*n) = A138526(n). a(4*n + 2) = 0.

Example

G.f. = 1 - q - q^3 + 2*q^4 - q^5 - 2*q^7 + 4*q^8 - 3*q^9 - 3*q^11 + 8*q^12 + ...

Mathematica

a[ n_] := SeriesCoefficient[ QPochhammer[ -q^5] QPochhammer[ q, q^2] / QPochhammer[ q^4], {q, 0, n}]; (* Michael Somos, Sep 02 2015 *)

Prog

(PARI) {a(n) = my(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A) * eta(x^10 + A)^3 / (eta(x^2 + A) * eta(x^4 + A) * eta(x^5 + A) * eta(x^20 + A)), n))};

Crossrefs

Cf. A036026, A138526.

Sequence in context: A329686 A261615 A146162 * A118208 A355650 A292892

Adjacent sequences: A147699 A147700 A147701 * A147703 A147704 A147705

Keyword

sign

Author

Michael Somos, Nov 10 2008

Status

approved