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A123344
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Expansion of (1+3*x)/(1+2*x).
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4
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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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0,3
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COMMENTS
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Inverse binomial transform ofA000034.
Hankel transform is [1,-3,0,0,0,0,0,0,0,0,...].
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LINKS
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FORMULA
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a(0)=1, a(n) = (-2)^(n-1) for n>0.
G.f.: (1+3*x)/(1+2*x).
G.f.: 1/U(0) where U(k)= 1 - x*(k+4) + x*(k+3)/U(k+1); (continued fraction, 1-step). -Sergei N. Gladkovskii,Oct 11 2012
a(n) = numerator((1/2 - n)!/sqrt(Pi)). -Peter Luschny,Jun 21 2020
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MAPLE
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MATHEMATICA
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Join[{1}, LinearRecurrence[{-2}, {1}, 32]] (*Ray Chandler,Aug 12 2015 *)
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PROG
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(PARI) x='x+O('x^50); Vec((1+3*x)/(1+2*x)) \\G. C. Greubel,Oct 12 2017
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CROSSREFS
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KEYWORD
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easy,sign
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AUTHOR
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STATUS
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approved
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