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Search: id:A134414
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| A134414 |
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Expansion of eta(q)^2 / (eta(q^2) * eta(q^4)^6) in powers of q. |
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+0
3
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| 1, -2, 0, 0, 8, -12, 0, 0, 39, -56, 0, 0, 152, -208, 0, 0, 513, -684, 0, 0, 1560, -2032, 0, 0, 4382, -5616, 0, 0, 11552, -14592, 0, 0, 28899, -36088, 0, 0, 69168, -85500, 0, 0, 159372, -195312, 0, 0, 355224, -431984, 0, 0, 768885, -928720, 0, 0, 1621296, -1946352, 0, 0, 3339201
(list; graph; listen)
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OFFSET
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-1,2
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REFERENCES
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K. Bringmann and K. Ono, An arithmetic formula for the partition function, Proc. Amer. Math. Soc. 135 (2007), 3507-3514. see p. 3507 Equ. (1.2)
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FORMULA
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Euler transform of period 4 sequence [ -2, -1, -2, 5, ...].
a(4*n+1) = a(4*n+2) = 0.
G.f.: x^(-1) * Product_{k>0} (1 - x^k) / ((1 + x^k) * (1 - x^(4*k))^6).
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EXAMPLE
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1/q - 2 + 8*q^3 - 12*q^4 + 39*q^7 - 56*q^8 + 152*q^11 - 208*q^12 + ...
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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)^2 / (eta(x^2 + A) * eta(x^4 + A)^6), n))}
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CROSSREFS
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A134415(n) = a(4*n-1). -2 * A134416(n) = a(4*n).
Sequence in context: A091933 A058347 A058547 this_sequence A113036 A000425 A010893
Adjacent sequences: A134411 A134412 A134413 this_sequence A134415 A134416 A134417
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Oct 26 2007
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