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A004295
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Expansion of (1+2*x+x^2)/(1-42*x+x^2).
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1
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1, 44, 1848, 77572, 3256176, 136681820, 5737380264, 240833289268, 10109260768992, 424348119008396, 17812511737583640, 747701144859504484, 31385635572361604688, 1317448992894327892412, 55301472065989409876616, 2321344377778660886925460
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OFFSET
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0,2
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REFERENCES
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P. de la Harpe, Topics in Geometric Group Theory, Univ. Chicago Press, 2000, p. 160, middle display.
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LINKS
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FORMULA
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a(n) = sqrt(11/10)*((21+2*sqrt(110))^(-n)*(-1+(21+2*sqrt(110))^(2*n))) for n>0.
a(n) = 42*a(n-1) - a(n-2) for n>2.
(End)
a(n) = -(-1)^(2^n)/2 + sqrt(22/5)*sinh(n*log(21+2*sqrt(110))) + 1/2. - Ilya Gutkovskiy, Apr 16 2016
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MATHEMATICA
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CoefficientList[Series[(1+2*x+x^2)/(1-42*x+x^2), {x, 0, 50}], x] (* Vincenzo Librandi, Feb 25 2012 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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