A146162 Expansion of eta(q^2)^2 * eta(q^5) / (eta(q) * eta(q^4)^2) 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

Links

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

Formula

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

G.f. is a period 1 Fourier series which satisfies f(-1 / (80 t)) = (4/5)^(1/2) g(t) where q = exp(2 Pi i t) and g() is g.f. for A146164.

a(4*n + 2) = 0.

Example

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[x^5]/(QPochhammer[x]* QPochhammer[ -x^2, x^2]^2), {x, 0, n}]; Table[a[n], {n, 0, 50}] (* G. C. Greubel, Dec 04 2017 *)

Prog

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

Crossrefs

A138526(n) = a(4*n). A145722(n) = a(4*n + 1). A146163(n) = a(4*n + 3).

Sequence in context: A329099 A329686 A261615 * A147702 A118208 A355650

Adjacent sequences: A146159 A146160 A146161 * A146163 A146164 A146165

Keyword

nonn

Author

Michael Somos, Oct 27 2008

Status

approved