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A146162 Expansion of eta(q^2)^2 * eta(q^5) / (eta(q) * eta(q^4)^2) in powers of q. 3
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 (list; graph; refs; listen; history; text; internal format)
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 A292892

Adjacent sequences:  A146159 A146160 A146161 * A146163 A146164 A146165

KEYWORD

nonn

AUTHOR

Michael Somos, Oct 27 2008

STATUS

approved

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Last modified August 2 05:02 EDT 2021. Contains 346409 sequences. (Running on oeis4.)