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A144704
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a(n) = 4^n*(1-2*n).
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5
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1, -4, -48, -320, -1792, -9216, -45056, -212992, -983040, -4456448, -19922944, -88080384, -385875968, -1677721600, -7247757312, -31138512896, -133143986176, -566935683072, -2405181685760, -10170482556928
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OFFSET
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0,2
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COMMENTS
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With the n-th term of A000984 (C(2n,n)) as numerator, |a(n)| is the denominator of the probability that a random walk with steps of +-1 will return to the starting point for the first time after 2n steps. - Shel Kaphan, Jan 12 2023
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LINKS
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FORMULA
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G.f.: (1-12*x)/(1-4*x)^2.
Sum_{n>=0} 1/a(n) = 1 - arctanh(1/2)/2.
Sum_{n>=0} (-1)^(n+1)/a(n) = 1 + arctan(1/2)/2. (End)
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MATHEMATICA
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LinearRecurrence[{8, -16}, {1, -4}, 30] (* Harvey P. Dale, Jun 12 2019 *)
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PROG
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(SageMath) [4^n*(1-2*n) for n in (0..30)] # G. C. Greubel, Jun 16 2022
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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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