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A193237
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G.f.: A(x) = ( Sum_{n>=0} 3^n*(2*n+1) * (-x)^(n*(n+1)/2) )^(-1/3).
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4
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1, 3, 18, 141, 1125, 9261, 78255, 673137, 5864238, 51592770, 457484382, 4082618376, 36627119109, 330070717935, 2985857903655, 27099681108948, 246666402397287, 2250904657271427, 20586440729350197, 188659279149885810, 1732045683183434379
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OFFSET
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0,2
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COMMENTS
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Compare to the q-series identity:
eta(x)^3 = Sum_{n>=0} (-1)^n*(2*n+1) * x^(n*(n+1)/2),
where eta(x) is Dedekind's eta(q) function without the q^(1/24) factor.
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LINKS
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Table of n, a(n) for n=0..20.
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EXAMPLE
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G.f.: A(x) = 1 + 3*x + 18*x^2 + 141*x^3 + 1125*x^4 + 9261*x^5 +...
where
1/A(x)^3 = 1 - 9*x - 45*x^3 + 189*x^6 + 729*x^10 - 2673*x^15 - 9477*x^21 + 32805*x^28 +...+ 3^n*(2*n+1)*(-x)^(n*(n+1)/2) +...
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PROG
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(PARI) {a(n)=local(S=sum(m=0, sqrtint(2*n), 3^m*(2*m+1)*(-x)^(m*(m+1)/2))+x*O(x^n)); polcoeff(S^(-1/3), n)}
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CROSSREFS
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Cf. A193236, A111984, A111983.
Sequence in context: A216492 A127129 A186266 * A212030 A107708 A224992
Adjacent sequences: A193234 A193235 A193236 * A193238 A193239 A193240
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna, Jul 18 2011
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STATUS
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approved
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