A146163 Expansion of q^(-3/4) * eta(q^2)^2 * eta(q^20) / (eta(q)^2 * eta(q^4)) in powers of q.

1, 2, 3, 6, 10, 16, 25, 38, 57, 84, 121, 172, 243, 338, 465, 636, 862, 1158, 1546, 2050, 2701, 3540, 4613, 5980, 7719, 9916, 12682, 16158, 20506, 25926, 32667, 41022, 51348, 64080, 79730, 98922, 122407, 151068, 185968, 228384, 279816, 342052

Offset: 0

Author

Michael Somos, Oct 27 2008

Keywords

• nonn

Examples

			q^3 + 2*q^7 + 3*q^11 + 6*q^15 + 10*q^19 + 16*q^23 + 25*q^27 + 38*q^31 + ...
		

Links

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

Programs

Mathematica

nmax = 50; CoefficientList[Series[Product[(1+x^k)^2 * (1-x^(20*k)) / (1-x^(4*k)), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jul 11 2016 *)
a[n_]:= SeriesCoefficient[QPochhammer[-q, q]^2*QPochhammer[q^20, q^20]/(QPochhammer[q^4, q^4]), {q, 0, n}]; Table[a[n], {n, 0, 50}] (* G. C. Greubel, Dec 05 2017 *)

PARI

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

Formula

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

a(n) ~ exp(2*Pi*sqrt(n/5)) / (4*5^(3/4)*n^(3/4)). - Vaclav Kotesovec, Jul 11 2016

a(n) = A146162(4*n + 3).