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A112298
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Expansion of (eta(q)eta(q^12))^3/(eta(q^2)eta(q^3)eta(q^4)eta(q^6)) in powers of q.
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2
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1, -3, 1, 3, 0, -3, 2, -3, 1, 0, 0, 3, 2, -6, 0, 3, 0, -3, 2, 0, 2, 0, 0, -3, 1, -6, 1, 6, 0, 0, 2, -3, 0, 0, 0, 3, 2, -6, 2, 0, 0, -6, 2, 0, 0, 0, 0, 3, 3, -3, 0, 6, 0, -3, 0, -6, 2, 0, 0, 0, 2, -6, 2, 3, 0, 0, 2, 0, 0, 0, 0, -3, 2, -6, 1, 6, 0, -6, 2, 0, 1, 0, 0, 6, 0, -6, 0, 0, 0, 0, 4, 0, 2, 0, 0, -3, 2, -9, 0, 3, 0, 0, 2, -6, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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FORMULA
| Euler transform of period 12 sequence [ -3, -2, -2, -1, -3, 0, -3, -1, -2, -2, -3, -2, ...].
Moebius transform is period 12 sequence [1, -4, 0, 6, -1, 0, 1, -6, 0, 4, -1, 0, ...].
Multiplicative with a(2^e) = 3(-1)^e if e>0, a(3^e)=1, a(p^e) = e+1 if p == 1 (mod 3), a(p^e) = (1+(-1)^e)/2 if p == 2 (mod 3).
G.f.: Sum_{k>0} kronecker(-3, k)*x^k*(1-x^k)^2/(1-x^(4k)).
a(6n+5) = 0, a(3n) = a(n).
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PROG
| (PARI) a(n)=if(n<1, 0, sumdiv(n, d, kronecker(-3, d)*[0, 1, -2, 1][n/d%4+1]))
(PARI) {a(n)=local(A); if(n<1, 0, n--; A=x*O(x^n); polcoeff( (eta(x+A)*eta(x^12+A))^3/ (eta(x^2+A)*eta(x^3+A)* eta(x^4+A)*eta(x^6+A)), n))}
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CROSSREFS
| -3*A093829(n) = a(2n). A033762(n) = a(2n+1). A129576(n) = a(3n+1). -3*A033687(n) = a(6n+2). A112604(n) = a(4n+1). A112605(n) = a(4n+3). A097195(n) = a(6n+1).
Sequence in context: A180021 A091422 A201659 * A011430 A073747 A127549
Adjacent sequences: A112295 A112296 A112297 * A112299 A112300 A112301
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KEYWORD
| sign,mult
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AUTHOR
| Michael Somos, Sep 02 2005
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