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

Author

Michael Somos, Oct 27 2008

Keywords

• nonn

Examples

			1 + q + q^3 + 2*q^4 + q^5 + 2*q^7 + 4*q^8 + 3*q^9 + 3*q^11 + 8*q^12 + ...
		

Links

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

Crossrefs

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

Programs

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 *)

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))}

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.