A030538 - OEIS

%I #15 Sep 08 2022 08:44:50

%S 1,2,6,29,219,2295,29359,418847,6323967,98276543,1549615167,

%T 24613132095,392371455295,6266462052671,100171654977855,

%U 1602013024405823,25626342538717503,409974560964700479,6559217646832380223,104944479835032512831,1679087657704374659391

%N (2^n+2)*(2^n+4)*(4^n+9*2^n+38)/720.

%H Vincenzo Librandi, <a href="/A030538/b030538.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (31,-310,1240,-1984,1024).

%F G.f.: -(684*x^4-777*x^3+254*x^2-29*x+1) / ((x-1) * (2*x-1) * (4*x-1) * (8*x-1) * (16*x-1)). - _Colin Barker_, Aug 03 2013

%t CoefficientList[Series[-(684 x^4 - 777 x^3 + 254 x^2 - 29 x + 1) / ((x - 1) (2 x - 1) (4 x - 1) (8 x-1) (16 x - 1)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Aug 04 2013 *)

%t LinearRecurrence[{31,-310,1240,-1984,1024},{1,2,6,29,219},30] (* _Harvey P. Dale_, Apr 22 2020 *)

%o (Magma) [(2^n+2)*(2^n+4)*(4^n+9*2^n+38)/720: n in [0..20]]; // _Vincenzo Librandi_, Aug 04 2013

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.