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A sum of decreasing powers.
2

%I #11 Sep 12 2024 19:32:27

%S 1,0,-2,24,382,3480,26398,183624,1217662,7844280,49595998,309603624,

%T 1915345342,11771312280,71987479198,438579414024,2664184199422,

%U 16146411375480,97676153291998,590010215086824,3559688013155902,21455704981601880,129219894496730398,777738831236334024

%N A sum of decreasing powers.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (20,-155,580,-1044,720).

%F a(n) = 6^n - 5^n - 4^n - 3^n + 3*2^n.

%F G.f.:(-1-636*x^4+516*x^3-153*x^2+20*x)/((6*x-1)*(4*x-1)*(3*x-1)*(2*x-1)*(5*x-1)) [From Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009]

%F a(0)=1, a(1)=0, a(2)=-2, a(3)=24, a(4)=382, a(n) = 20*a(n-1) - 155*a(n-2) + 580*a(n-3) - 1044*a(n-4) + 720*a(n-5). - _Harvey P. Dale_, Sep 15 2014

%F E.g.f.: exp(2*x)*(exp(4*x) - exp(3*x) - exp(2*x) - exp(x) + 3). - _Elmo R. Oliveira_, Sep 12 2024

%t Table[6^n-5^n-4^n-3^n+3*2^n,{n,0,30}] (* or *) LinearRecurrence[{20,-155,580,-1044,720},{1,0,-2,24,382},30] (* _Harvey P. Dale_, Sep 15 2014 *)

%Y Binomial transform of A081684.

%K easy,sign

%O 0,3

%A _Paul Barry_, Mar 30 2003

%E a(23) from _Elmo R. Oliveira_, Sep 12 2024