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A146165 Expansion of q^(1/4) * eta(q^5)^2 * eta(q^20) / (eta(q^4) * eta(q^10)^2) in powers of q. 1
1, 0, 0, 0, 1, -2, 0, 0, 2, -2, 1, 0, 3, -4, 1, -2, 5, -6, 2, -2, 10, -10, 3, -4, 14, -16, 5, -6, 21, -24, 11, -10, 31, -34, 15, -18, 45, -50, 23, -26, 67, -70, 34, -38, 93, -104, 50, -56, 130, -140, 77, -80, 179, -196, 107, -120, 245, -264, 151, -164, 338, -360, 210, -230, 451, -488, 290, -314, 604, -650, 404 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,6
LINKS
FORMULA
Euler transform of period 20 sequence [ 0, 0, 0, 1, -2, 0, 0, 1, 0, 0, 0, 1, 0, 0, -2, 1, 0, 0, 0, 0, ...].
EXAMPLE
q + q^17 - 2*q^21 + 2*q^33 - 2*q^37 + q^41 + 3*q^49 - 4*q^53 + q^57 + ...
MATHEMATICA
QP = QPochhammer; s = QP[q^5]^2*(QP[q^20]/(QP[q^4]*QP[q^10]^2)) + O[q]^80; CoefficientList[s, q] (* Jean-François Alcover, Nov 25 2015 *)
PROG
(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^5 + A)^2 * eta(x^20 + A) / (eta(x^4 + A) * eta(x^10 + A)^2), n))}
CROSSREFS
Convolution inverse of A146164.
Sequence in context: A356018 A107502 A230419 * A308831 A277327 A277328
KEYWORD
sign
AUTHOR
Michael Somos, Oct 27 2008
STATUS
approved

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Last modified July 13 14:24 EDT 2024. Contains 374284 sequences. (Running on oeis4.)