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A185202
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G.f. A(x) satisfies: x = Sum_{n>=0} -(-A(x))^A000069(n), where A000069 is the odious numbers.
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0
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1, 1, 2, 6, 20, 70, 255, 961, 3717, 14663, 58758, 238524, 978844, 4054152, 16924986, 71145392, 300876074, 1279225578, 5464762332, 23444755016, 100968932096, 436355661280, 1891770895672, 8225329914410, 35858439130786, 156708088823482, 686392551655052
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OFFSET
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1,3
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COMMENTS
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The odious numbers (A000069) have an odd number of 1's in their binary expansion.
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LINKS
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FORMULA
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Equals the series reversion of the g.f. of the Thue-Morse sequence (A010060) evaluated at x = -x.
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EXAMPLE
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G.f.: A(x) = x + x^2 + 2*x^3 + 6*x^4 + 20*x^5 + 70*x^6 + 255*x^7 +...
Series reversion of the g.f. yields:
G(x) = x - x^2 - x^4 + x^7 - x^8 + x^11 + x^13 - x^14 - x^16 + x^19 + x^21 - x^22 + x^25 +..+ -(-x)^A000069(n) +...
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PROG
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(PARI) {odious(n)=if(n==0, 1, if(n%2==0, odious(n/2)+n, -odious((n-1)/2)+3*n))}
{a(n)=polcoeff(serreverse(sum(k=1, n+1, -(-x)^odious(k-1)+x^2*O(x^n))), n)}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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