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A146163 Expansion of q^(-3/4) * eta(q^2)^2 * eta(q^20) / (eta(q)^2 * eta(q^4)) in powers of q. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 22 04:27 EST 2020. Contains 331133 sequences. (Running on oeis4.)