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A111335
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Let qf(a,q) = Product_{j>=0} (1 - a*q^j); g.f. is qf(q^3,q^4)/qf(q,q^4).
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4
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1, 1, 1, 0, 0, 1, 1, 0, -1, 0, 2, 1, -1, -1, 1, 2, -1, -2, 1, 3, 1, -3, -1, 3, 1, -3, -2, 4, 4, -3, -4, 3, 5, -3, -7, 2, 9, 0, -9, -1, 10, 3, -11, -5, 12, 8, -11, -10, 10, 12, -11, -15, 11, 19, -7, -21, 6, 24, -5, -28, 1, 31, 4, -33, -8, 36, 12, -38, -18, 40, 27, -40, -33, 40, 39, -40, -49, 38, 60, -34, -67, 30, 75, -25, -87, 18, 98
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OFFSET
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0,11
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LINKS
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FORMULA
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Euler transform of period 4 sequence [1, 0, -1, 0, ...]. - Michael Somos, Nov 10 2005
G.f.: Product_{k>0} (1-x^(2k-1))^((-1)^k). - Michael Somos, Nov 11 2005
G.f.: exp( Sum_{k >= 1} 1/(k*(x^k + x^(-k)) ). - Peter Bala, Sep 28 2023
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MAPLE
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# Uses EulerTransform from A358369.
a := EulerTransform(BinaryRecurrenceSequence(0, -1)):
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PROG
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(PARI) {a(n)=if(n<0, 0, polcoeff( prod(k=0, n\2, (1-x^(2*k+1))^(-(-1)^k), 1+x*O(x^n)), n))} /* Michael Somos, Nov 11 2005 */
(Sage) # uses[EulerTransform from A166861]
b = BinaryRecurrenceSequence(0, -1)
a = EulerTransform(b)
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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