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A004296
Expansion of (1+2*x+x^2)/(1-50*x+x^2).
1
1, 52, 2600, 129948, 6494800, 324610052, 16224007800, 810875779948, 40527564989600, 2025567373700052, 101237841120013000, 5059866488626949948, 252892086590227484400, 12639544463022747270052, 631724331064547136018200, 31573577008764334053639948
OFFSET
0,2
REFERENCES
P. de la Harpe, Topics in Geometric Group Theory, Univ. Chicago Press, 2000, p. 160, middle display.
LINKS
J. M. Alonso, Growth functions of amalgams, in Alperin, ed., Arboreal Group Theory, Springer, pp. 1-34, esp. p. 32.
FORMULA
From Colin Barker, Apr 16 2016: (Start)
a(n) = (sqrt(13/3)*(25+4*sqrt(39))^(-n)*(-1+(25+4*sqrt(39))^(2*n)))/2 for n>0.
a(n) = 50*a(n-1) - a(n-2) for n>2.
(End)
a(n) = (-3*(-1)^(2^n) + 2*sqrt(39)*sinh(n*log(25+4*sqrt(39))) + 3)/6. - Ilya Gutkovskiy, Apr 16 2016
MATHEMATICA
CoefficientList[Series[(1+2*x+x^2)/(1-50*x+x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Feb 25 2012 *)
PROG
(PARI) Vec((1+2*x+x^2)/(1-50*x+x^2)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012
CROSSREFS
Sequence in context: A342898 A215595 A134552 * A097837 A247628 A370188
KEYWORD
nonn,easy
STATUS
approved