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A227209 Expansion of 1/((1-x)^2*(1-2x)*(1-4x)). 0

%I

%S 1,8,43,198,849,3516,14311,57746,231997,930024,3724179,14904894,

%T 59635945,238576532,954371647,3817617642,15270732693,61083455040,

%U 244334868715,977341571990,3909370482241,15637490317548

%N Expansion of 1/((1-x)^2*(1-2x)*(1-4x)).

%C This sequence was chosen to illustrate a method of solution.

%C In general, for the expansion of 1/((1-t)^2)*(1-s)(1-r)) with r>s>t we have the formula: a(n) = ( K*r^(n+3) + L*s^(n+3) + M*t^(n+3) + N*t^(n+3) )/D where K,L,M,N,D, have the following values:

%C K = (s-t)^2;

%C L = -(r-t)^2;

%C M = (r-s)*(r+s-2*t);

%C N = (r-t)*(s-t)*(r-s)*(n+3);

%C D = (r-s)*(r-t)^2*(s-t)^2.

%C Directly using formula we get a(n) = ( 4^(n+3) - 9*2^(n+3) + 8 + 6*(n+3) )/18. After transformation we obtain previous formula.

%F a(n) = ( 4^(n+3) - 9*2^(n+3) + 6*n + 26 )/18.

%t nn = 25; CoefficientList[Series[1/((1 - x)^2*(1 - 2 x)*(1 - 4 x)), {x, 0, nn}], x] (* _T. D. Noe_, Sep 19 2013 *)

%Y Cf. A229026.

%K nonn,easy

%O 1,2

%A _Yahia Kahloune_, Sep 19 2013

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Last modified August 6 00:46 EDT 2021. Contains 346493 sequences. (Running on oeis4.)