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A161495 Expansion of x*(3*x-1)*(x-3)/(1-15*x+32*x^2-15*x^3+x^4). 1

%I #13 Feb 28 2018 11:31:12

%S 3,35,432,5405,67773,850080,10663107,133755235,1677792528,21045816925,

%T 263993558397,3311470367040,41538271098243,521045872287395,

%U 6535871471114352,81984366749625245,1028391763981932093

%N Expansion of x*(3*x-1)*(x-3)/(1-15*x+32*x^2-15*x^3+x^4).

%C Proposed by R. Guy in the seqfan list, Mar 29 2009.

%H Vincenzo Librandi, <a href="/A161495/b161495.txt">Table of n, a(n) for n = 1..900</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (15,-32,15,-1).

%F G.f. x*(3*x-1)*(x-3)/(1-15*x+32*x^2-15*x^3+x^4).

%F a(n) = 15*a(n-1)-32*a(n-2)+15*a(n-3)-a(n-4).

%F (a(n))^2 = A161159(n)*A004254(n) = A003739(n)/(5*(A001906(n))^2).

%t Rest[CoefficientList[Series[x(3x-1)(x-3)/(1-15x+32x^2-15x^3+x^4), {x,0,30}], x]] (* or *) LinearRecurrence[{15,-32,15,-1},{3,35,432,5405},30] (* _Harvey P. Dale_, Nov 03 2011 *)

%K nonn,easy

%O 1,1

%A _R. J. Mathar_, Jun 11 2009

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