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A143161 Expansion of q^(1/6) * eta(q)^2 / (eta(q^2) * eta(q^4)) in powers of q. +0
1
1, -2, 0, 0, 3, -2, 0, 0, 4, -6, 0, 0, 7, -8, 0, 0, 13, -14, 0, 0, 19, -20, 0, 0, 29, -34, 0, 0, 43, -46, 0, 0, 62, -70, 0, 0, 90, -96, 0, 0, 126, -138, 0, 0, 174, -186, 0, 0, 239, -262, 0, 0, 325, -346, 0, 0, 435, -472, 0, 0, 580, -620, 0, 0, 769, -826, 0, 0, 1007, -1072, 0, 0, 1313, -1408, 0, 0, 1702 (list; graph; listen)
OFFSET

0,2

FORMULA

Expansion of chi(-q)^2 * chi(-q^2) in powers of q where chi() is a Ramanujan theta function.

Euler transform of period 4 sequence [ -2, -1, -2, 0, ...].

a(4*n + 2) = a(4*n + 3) = 0.

G.f.: (Product_{k>0} (1 + x^k)^2 * (1 + x^(2*k)))^-1.

EXAMPLE

1/q - 2*q^5 + 3*q^23 - 2*q^29 + 4*q^47 - 6*q^53 + 7*q^71 - 8*q^77 + ...

PROGRAM

(PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x + A)^2 / eta(x^2 + A) / eta(x^4 + A), n))}

CROSSREFS

A029552(n) = a(4*n). -2 * A098613(n) = a(4*n + 1).

Sequence in context: A167634 A113411 A125095 this_sequence A142886 A099026 A053202

Adjacent sequences: A143158 A143159 A143160 this_sequence A143162 A143163 A143164

KEYWORD

sign

AUTHOR

Michael Somos, Jul 27 2008

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Last modified December 20 00:58 EST 2009. Contains 171054 sequences.


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