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Search: id:A116498
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| A116498 |
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Expansion of psi(-q)/psi(-q^2) in powers of q where psi() is a Ramanujan theta function. |
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1
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| 1, -1, 1, -2, 1, -2, 3, -3, 4, -5, 6, -7, 8, -9, 11, -13, 16, -18, 21, -24, 27, -32, 36, -41, 48, -54, 61, -70, 78, -88, 100, -112, 127, -143, 159, -179, 199, -222, 248, -276, 308, -342, 380, -421, 465, -516, 570, -629, 697, -767, 845, -932, 1022, -1124, 1236, -1355, 1488, -1631, 1785, -1954, 2136
(list; graph; listen)
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OFFSET
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0,4
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FORMULA
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Expansion of q^(1/8)*eta(q)*eta(q^4)^2/(eta(q^2)^2*eta(q^8)) in powers of q.
Euler transform of period 8 sequence [ -1,1,-1,-1,-1,1,-1,0,...].
Given g.f. A(x), then B(x)=A(x^8)/x satisfies 0=f(B(x),B(x^3)) where f(u,v)=3*u*v -(u+v^3)*(v-u^3).
G.f.: Product_{k>0} (1+x^(2k))/((1+x^k)(1+x^(4k))) = (Sum_{k>0} (-x)^((k^2-k)/2))/(Sum_{k>0} (-x^2)^((k^2-k)/2)).
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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^4+A)^2/eta(x^2+A)^2/eta(x^8+A), n))}
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CROSSREFS
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a(n)=(-1)^n*A070048(n).
Sequence in context: A102885 A138585 A070048 this_sequence A143472 A015739 A015746
Adjacent sequences: A116495 A116496 A116497 this_sequence A116499 A116500 A116501
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Feb 18 2006
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