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Search: id:A109389
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| A109389 |
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Expansion of q^(-1/12)eta(q)eta(q^6)/(eta(q^2)eta(q^3)) in powers of q. |
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+0
1
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| 1, -1, 0, 0, 0, -1, 1, -1, 1, 0, 0, -1, 2, -2, 1, 0, 1, -2, 3, -3, 2, -1, 1, -3, 5, -5, 3, -1, 2, -5, 7, -7, 5, -3, 3, -7, 11, -11, 7, -4, 6, -11, 15, -15, 11, -7, 8, -15, 22, -22, 15, -10, 13, -22, 30, -30, 23, -16, 18, -30, 42, -42, 31, -22, 27, -43, 56, -56, 44, -33, 37, -57, 77, -77, 59, -45, 53, -79, 101, -101, 82, -64
(list; graph; listen)
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OFFSET
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0,13
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FORMULA
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Euler transform of period 6 sequence [ -1, 0, 0, 0, -1, 0, ...].
G.f.: 1/(Product_{k>0} (1+^(2k-1)+x^(4k-2))) = Product_{k>0} (1-x^(6k-1))(1-x^(6k-5)) = Product_{k>0} (1-x^k+x^(2k)) (where 1-x+x^2 is 6th cyclotomic polynomial).
Given g.f. A(x), then B(x)=x*A(x^12) satisfies 0=f(B(x), B(x^2), B(x^4)) where f(u, v, w)=(v^2+u^4)*(v^2+w^4)-2*v^4*(1-v*u^2*w^2).
Expansion of G(x^6) * H(x) - x * G(x) * H(x^6) where G(), H() are Rogers-Ramanujan functions.
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EXAMPLE
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q - q^13 - q^61 + q^73 - q^85 + q^97 - q^133 + 2*q^145 - 2*q^157 + q^169 + ...
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PROGRAM
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(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x+A)*eta(x^6+A)/eta(x^2+A)/eta(x^3+A), n))}
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CROSSREFS
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Cf. a(n)=(-1)^n*A098884(n).
Sequence in context: A123149 A061926 A053188 this_sequence A098884 A039800 A109246
Adjacent sequences: A109386 A109387 A109388 this_sequence A109390 A109391 A109392
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Jun 26 2005
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