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Search: id:A133637
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| A133637 |
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Expansion of q^(-1) * psi(-q) / psi(-q^3)^3 in powers of q where psi() is a Ramanujan theta function. |
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3
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| 1, -1, 0, 2, -3, 0, 4, -6, 0, 10, -12, 0, 20, -24, 0, 36, -45, 0, 64, -78, 0, 112, -132, 0, 189, -222, 0, 308, -363, 0, 492, -576, 0, 778, -900, 0, 1210, -1392, 0, 1844, -2121, 0, 2776, -3180, 0, 4144, -4716, 0, 6114, -6936, 0, 8914, -10098, 0, 12884, -14550, 0, 18484, -20796, 0, 26302
(list; graph; listen)
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OFFSET
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-1,4
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FORMULA
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Expansion of ( 3 * c(q^2) ) / ( c(q) * c(q^4) ) in powers of q where c() is a cubic AGM function.
Euler transform of period 12 sequence [ -1, 0, 2, -1, -1, 0, -1, -1, 2, 0, -1, 2, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (12 t)) = (3/4)^(1/2) (t/i)^(-1) g(t) where q = exp(2 pi i t) and g(t) is g.f. for A132974.
a(3*n+1) = 0.
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EXAMPLE
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1/q - 1 + 2*q^2 - 3*q^3 + 4*q^5 - 6*q^6 + 10*q^8 - 12*q^9 + 20*q^11 - ...
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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^4 + A) * eta(x^6 + A)^3 / ( eta(x^2 + A) * eta(x^3 + A)^3 * eta(x^12 + A)^3 ), n))}
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CROSSREFS
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A132974(n) = - a(3*n). Convolution inverse of A113427.
Sequence in context: A011150 A100112 A091246 this_sequence A010340 A049275 A121598
Adjacent sequences: A133634 A133635 A133636 this_sequence A133638 A133639 A133640
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Sep 18 2007
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