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A141531
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Inverse binomial transform of A001651.
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3
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1, 1, 1, -2, 4, -8, 16, -32, 64, -128, 256, -512, 1024, -2048, 4096, -8192, 16384, -32768, 65536, -131072, 262144, -524288, 1048576, -2097152, 4194304, -8388608, 16777216, -33554432, 67108864, -134217728, 268435456, -536870912, 1073741824, -2147483648
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OFFSET
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0,4
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LINKS
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FORMULA
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a(n) = (-2)^n/4 = (-1)^n*A000079(n-2), n > 1.
O.g.f.: (1 + 3*x + 3*x^2)/(1 + 2*x). - R. J. Mathar, Aug 27 2008
a(n) = -2*a(n-1) for n >= 3; a(0)=1, a(1)=1, a(2)=1. - Harvey P. Dale, May 04 2012
G.f.: x+1/Q(0) where Q(k) = 1 + x*(k+1)/(1 - 1/(1 - (k+1)/Q(k+1))); (continued fraction). - Sergei N. Gladkovskii, Sep 23 2012
G.f.: 1+x/U(0) where U(k) = 1 - x*(k+4) + x*(k+3)/U(k+1); (continued fraction). - Sergei N. Gladkovskii, Oct 11 2012
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MATHEMATICA
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CoefficientList[Series[(1+3x+3x^2)/(1+2x), {x, 0, 40}], x] (* or *) Join[ {1, 1}, NestList[-2#&, 1, 38]] (* Harvey P. Dale, May 04 2012 *)
Join[{1, 1}, LinearRecurrence[{-2}, {1}, 32]] (* Ray Chandler, Aug 12 2015 *)
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PROG
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(PARI) Vec((1 + 3*x + 3*x^2)/(1 + 2*x) + O(x^40)) \\ Andrew Howroyd, Nov 03 2018
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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