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

0,2

Links

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

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).

Example

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

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 *)

Prog

(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))}

Crossrefs

Sequence in context: A324742 A260599 A280908 * A101277 A262984 A201077

Adjacent sequences: A146160 A146161 A146162 * A146164 A146165 A146166

Keyword

nonn

Author

Michael Somos, Oct 27 2008

Status

approved