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 A113946 Series expansion of Farey rational polynomial based on A112627. 0
 1, 5, 23, 81, 367, 1297, 5871, 20753, 93935, 332049, 1502959, 5312785, 24047343, 85004561, 384757487, 1360072977, 6156119791, 21761167633, 98497916655, 348178682129, 1575966666479, 5570858914065, 25215466663663, 89133742625041 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Polynomial expanded is constant*(x+1/2)^2*(1+2x)/(1-x-16x^2+16x^3) the Jasinski rational polynomial p[x_] = (9/32)*(x + 1/2)^3/((x - 1/4)*(x + 1/4)*(x + 1)) f[x_] := 1/p[x] /; 0 <= x <= 1/2 f[x_] := p[x] /; 1/2 < x <= 1 gives a Farey like function with maximum at 1. LINKS Index to sequences with linear recurrences with constant coefficients, signature (-1,16,16). FORMULA b(n)=coefficient series expansion of (9/32)*(x + 1/2)^3/((x - 1/4)*(x + 1/4)*(x + 1)) a(n) = (-16/9)*b(n) a(n) = (5*(-4)^n+4*(-1)^n+81*4^n)/60 for n>0. G.f.: -(2*x+1)^3 / ((x+1)*(4*x-1)*(4*x+1)). [Colin Barker, Dec 03 2012] MATHEMATICA b = -(16/9)*ReplacePart[Table[Coefficient[Series[(9/32)*(x + 1/2)^3/((x - 1/4)*(x + 1/4)*(x + 1)), {x, 0, 30}], x^n], {n, 0, 30}], -9/16, 1] CROSSREFS Cf. A112627. Sequence in context: A211809 A211922 A139209 * A193696 A147359 A034447 Adjacent sequences:  A113943 A113944 A113945 * A113947 A113948 A113949 KEYWORD nonn,easy AUTHOR Roger L. Bagula, Jan 31 2006 STATUS approved

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