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Search: id:A094363
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| A094363 |
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Expansion of (eta(q)eta(q^39))/(eta(q^3)eta(q^13)) in powers of q. |
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+0
1
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| 1, -1, -1, 1, -1, 0, 2, -1, -1, 3, -2, -1, 4, -2, -3, 4, -3, -3, 8, -4, -5, 9, -4, -6, 13, -6, -7, 14, -10, -9, 20, -9, -12, 24, -13, -13, 32, -16, -19, 39, -23, -24, 50, -26, -27, 60, -35, -34, 78, -41, -42, 91, -49, -54, 111, -60, -65, 138, -73, -78, 167, -84, -95, 199, -107, -111, 236, -128, -135, 282, -147, -159, 338
(list; graph; listen)
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OFFSET
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1,7
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COMMENT
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Euler transform of period 39 sequence [ -1,-1,0,-1,-1,0,-1,-1,0,-1,-1,0,0,-1,0,-1,-1,0,-1,-1,0,-1,-1,0,-1,0,0,-1,-1,0,-1,-1,0,-1,-1,0,-1,-1,0,...].
G.f. A(x) satisfies 0=f(A(x),A(x^2))=f(1/A(x),1/A(x^2)) where f(u,v)=u^3+v^3+2uv(u+v)-u^2v^2-uv.
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FORMULA
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G.f.: x Product_{k>0} (1-x^k)(1-x^(39k))/((1-x^(3k))(1-x^(13k))).
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PROGRAM
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(PARI) a(n)=local(A); if(n<1, 0, n--; A=x*O(x^n); polcoeff(eta(x+A)*eta(x^39+A)/eta(x^3+A)/eta(x^13+A), n))
(PARI)
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CROSSREFS
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Sequence in context: A079673 A124829 A093394 this_sequence A124832 A137569 A089177
Adjacent sequences: A094360 A094361 A094362 this_sequence A094364 A094365 A094366
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KEYWORD
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sign
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AUTHOR
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Michael Somos, May 03 2004
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