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A132041
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Expansion of (eta(q)* eta(q^2)/( eta(q^5)* eta(q^10)))^2 in powers of q.
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0
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1, -2, -3, 6, 2, 2, -5, -16, 12, 2, 17, -10, -48, 56, 10, 24, -35, -126, 106, 14, 94, -70, -284, 296, 60, 152, -175, -620, 536, 80, 398, -320, -1243, 1218, 216, 652, -680, -2422, 2122, 328, 1435, -1190, -4470, 4240, 734, 2312, -2285, -8120, 7130, 1112, 4549, -3850, -14178, 13132, 2210
(list; graph; refs; listen; history; internal format)
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OFFSET
| -1,2
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FORMULA
| Euler transform of period 10 sequence [ -2, -4, -2, -4, 0, -4, -2, -4, -2, 0, ...].
G.f. is a Fourier series which satisfies f(-1/(10 t)) = 25/ f(t) where q = exp(2 pi i t).
G.f.: (Product_{k>0} (1-x^k)* (1-x^(2k))/( (1-x^(5k))* (1-x^(10k))))^2.
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EXAMPLE
| 1/q - 2 - 3*q + 6*q^2 + 2*q^3 + 2*q^4 - 5*q^5 - 16*q^6 + 12*q^7 + ...
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PROG
| (PARI) {a(n)= local(A); if(n<-1, 0, n++; A= x*O(x^n); polcoeff( (eta(x+A)* eta(x^2+A)/ eta(x^5+A)/ eta(x^10+A))^2, n))}
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CROSSREFS
| Cf. A058099(n)= a(n) unless n=0.
Sequence in context: A002171 A138515 A107410 * A153634 A073546 A115033
Adjacent sequences: A132038 A132039 A132040 * A132042 A132043 A132044
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KEYWORD
| sign
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AUTHOR
| Michael Somos, Aug 07 2007
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