A113923 Expansion of 3*(2-x)^2/(1-x).

12, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3

Offset

0,1

Links

Table of n, a(n) for n=0..34.

Formula

b(n) = coefficient expansion of -3*(-2 + x^2)^2/(49*x^2 *(-1 + x^2)), a(n) = 49*b(n).

Mathematica

k[n_] = -(-1 + 2^(-n))^(-n)* (-2 + 2^(-n))^n *(-1 + 2^n) j[x_, n_] = (x^n - 2)^n/(k[n]*x^n*(x^n - 1)^(n - 1)) (* Farey-like function *) f[x_] := 1/(j[x, 2]) /; 0 <= x <= 1/2 f[x_] := j[x, 2] /; 1/2 < x <= 2 ff[x_] = f[Mod[Abs[x], 2]] Plot[f[Mod[Abs[x], 2]], {x, 0, 2}] (*n=2 level*) b = 49*ReplacePart[Table[Coefficient[Series[ -3* (-2 + x^2)^2/(49* x^2 (-1 + x^2)), {x, 0, 30}], x^n], {n, -2, 30}], 3/49, 3] (* removing the zeros *) c = Flatten[Table[If[b[[n]] > 0, b[[n]], {}], {n, 1, Length[b]}]]

Crossrefs

Sequence in context: A322731 A370330 A370430 * A370526 A048730 A307163

Adjacent sequences: A113920 A113921 A113922 * A113924 A113925 A113926

Keyword

nonn,easy,less

Author

Roger L. Bagula, Jan 30 2006

Extensions

NAME simplified by R. J. Mathar, May 25 2023

Status

approved