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%I #8 Jul 04 2022 12:28:49
%S 1,4,14,52,203,808,3232,12936,51765,207100,828466,3313964,13255999,
%T 53024192,212097028,848388448,3393554217,13574217396,54296870230,
%U 217187481700,868749927731,3474999712024,13899998849384,55599995399032,222399981597853,889599926393388,3558399705575802,14233598822305756
%N Expansion of (1-2*x)^2/((1-x)^4*(1-4*x)).
%C Suggested by A262592.
%H Colin Barker, <a href="/A262594/b262594.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (8,-22,28,-17,4).
%F From _Colin Barker_, Oct 23 2015: (Start)
%F a(n) = 8*a(n-1)-22*a(n-2)+28*a(n-3)-17*a(n-4)+4*a(n-5) for n>4.
%F a(n) = (34+2^(7+2*n)+93*n+18*n^2-9*n^3)/162.
%F (End)
%t CoefficientList[Series[(1-2x)^2/((1-x)^4(1-4x)),{x,0,40}],x] (* or *) LinearRecurrence[ {8,-22,28,-17,4},{1,4,14,52,203},40] (* _Harvey P. Dale_, Jul 04 2022 *)
%o (PARI) a(n) = (34+2^(7+2*n)+93*n+18*n^2-9*n^3)/162 \\ _Colin Barker_, Oct 23 2015
%o (PARI) Vec((1-2*x)^2/((1-x)^4*(1-4*x)) + O(x^40)) \\ _Colin Barker_, Oct 23 2015
%Y Cf. A262592.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Oct 22 2015