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A099138
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a(n) = 6^(n-1)*J(n), where J(n) = A001045(n).
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1
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0, 1, 6, 108, 1080, 14256, 163296, 2006208, 23794560, 287214336, 3436494336, 41298398208, 495217981440, 5944792559616, 71324450021376, 855971764420608, 10271190988062720, 123257112966660096, 1479068428940476416
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OFFSET
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0,3
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COMMENTS
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In general k^(n-1)*J(n), where J(n) = A001045(n), is given by ((2*k)^n - (-k)^n)/(3*k) with g.f. x/((1+k*x)*(1-2*k*x)).
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LINKS
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FORMULA
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G.f.: x/((1+6*x)*(1-12*x)).
a(n) = 6^(n-1)*Sum_{k=0..floor((n-1)/2)} binomial(n-k-1, k) * 2^k.
a(n) = (12^n - (-6)^n)/18.
E.g.f.: (1/18)*(exp(12*x) - exp(-6*x)). - G. C. Greubel, Feb 18 2023
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MATHEMATICA
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LinearRecurrence[{6, 72}, {0, 1}, 40] (* G. C. Greubel, Feb 18 2023 *)
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PROG
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(Magma) [(12^n - (-6)^n)/18: n in [0..40]]; // G. C. Greubel, Feb 18 2023
(SageMath) [(12^n - (-6)^n)/18 for n in range(41)] # G. C. Greubel, Feb 18 2023
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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