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A115235
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Expansion of eta(q)^2*eta(q^9)*eta(q^18)/(eta(q^2)*eta(q^3)) in powers of q.
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0
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1, -2, 0, 1, 0, 0, 2, -2, 0, 0, 0, 0, 2, -4, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 1, -4, 0, 2, 0, 0, 2, -2, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 3, -2, 0, 2, 0, 0, 0, -4, 0, 0, 0, 0, 2, -4, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 2, -4, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, -6, 0, 1, 0, 0, 2, -4, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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FORMULA
| Euler transform of period 18 sequence [ -2, -1, -1, -1, -2, 0, -2, -1, -2, -1, -2, 0, -2, -1, -1, -1, -2, -2, ...].
Moebius transform is period 18 sequence [1, -3, -1, 3, -1, 3, 1, -3, 0, 3, -1, -3, 1, -3, 1, 3, -1, 0, ...].
a(n) is multiplicative with a(2^e) = (-1+3*(-1)^e)/2, a(3^e) = 0^e, a(p^e) = e+1 if p == 1 (mod 6), a(p^e) = (1+(-1)^e)/2 if p == 5 (mod 6).
a(3n+1)=A033687(n), a(6n+2)=-2*A033687(n), a(3n)=a(6n+5)=0. a(4n)=a(n).
G.f.: Sum_{k} x^(3k+1)*(1-2*x^(3k+1))/(1-x^(18k+6)).
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EXAMPLE
| q -2*q^2 +q^4 +2*q^7 -2*q^8 +2*q^13 -4*q^14 +q^16 +2*q^19 +...
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PROG
| (PARI) {a(n)=local(A); if(n<1, 0, n--; A=x*O(x^n); polcoeff( eta(x+A)^2*eta(x^9+A)*eta(x^18+A)/eta(x^2+A)/eta(x^3+A), n))}
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CROSSREFS
| Sequence in context: A106602 A106594 A143251 * A160973 A036853 A036852
Adjacent sequences: A115232 A115233 A115234 * A115236 A115237 A115238
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KEYWORD
| sign,mult
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AUTHOR
| Michael Somos, Jan 17 2006
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