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A166149
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a(n) = (5^n + 10*(-6)^n)/11.
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5
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1, -5, 35, -185, 1235, -6785, 43835, -247385, 1562435, -8983985, 55857035, -325376585, 2001087635, -11762385185, 71795014235, -424666569785, 2578516996835, -15318514090385, 92674023995435, -552229446706985
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OFFSET
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0,2
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COMMENTS
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Fourth binomial transform of A014992.
Sixth binomial transform is A001020 preceded by 1.
Lim_{n -> infinity} a(n)/a(n-1) = -6. (End)
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LINKS
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FORMULA
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a(n) = 30*a(n-2)-a(n-1), a(0)= 1, a(1)= -5.
G.f.: (1-4x)/(1+x-30*x^2).
a(n) = Sum_{k=0..n} A112555(n,k)*(-6)^k.
E.g.f.: (1/11)*(exp(5*x) + 10*exp(-6*x)). - G. C. Greubel, May 01 2016
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MATHEMATICA
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CoefficientList[Series[(1-4x)/(1+x-30x^2), {x, 0, 40}], x] (* Harvey P. Dale, Mar 11 2011 *)
LinearRecurrence[{-1, 30}, {1, -5}, 20] (* Harvey P. Dale, Jan 20 2022 *)
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PROG
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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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