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Search: id:A091561
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| A091561 |
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Expansion of (1-2x-sqrt(1-4x+4x^2-4x^3))/(2x^2). |
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+0
3
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| 1, 2, 4, 9, 22, 56, 146, 388, 1048, 2869, 7942, 22192, 62510, 177308, 506008, 1451866, 4185788, 12119696, 35227748, 102753800, 300672368, 882373261, 2596389190, 7658677856, 22642421206, 67081765932, 199128719896, 592179010350
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OFFSET
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1,2
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FORMULA
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G.f.: (1-2x-sqrt(1-4x+4x^2-4x^3))/(2x^2).
a(n)=2*a(n-1)+a(1)*a(n-3)+a(2)*a(n-4)+...+a(n-3)*a(1) for n>1.
Series reversion of g.f. A(x) is -A(-x).
G.f. A(x) satisfies 0=f(x, A(x)) where f(x, y)=(xy)^2+2(xy)-(y-x).
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PROGRAM
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(PARI) a(n)=polcoeff((1-2*x-sqrt(1-4*x+4*x^2-4*x^3+x^3*O(x^n)))/2, n+2)
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CROSSREFS
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Cf. A025247, A025265.
Sequence in context: A055588 A088456 A152225 this_sequence A025265 A037245 A143017
Adjacent sequences: A091558 A091559 A091560 this_sequence A091562 A091563 A091564
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Jan 20 2004
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