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a(n) = (6^n - 5^n - 4^n - 3^n + 4*2^n)/2.
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%I #20 Sep 13 2024 08:14:52

%S 1,1,1,16,199,1756,13231,91876,608959,3922396,24798511,154802836,

%T 957674719,5885660236,35993747791,219289723396,1332092132479,

%U 8073205753276,48838076777071,295005107805556,1779844007102239,10727852491849516,64609947250462351,388869415622361316

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

%C Inverse binomial transform of A081680.

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

%F G.f.: (1-19*x+136*x^2-429*x^3+498*x^4)/((1-2*x)*(1-3*x)*(1-4*x)*(1-5*x)*(1-6*x)). - _Bruno Berselli_, Dec 15 2010

%F From _Elmo R. Oliveira_, Sep 12 2024: (Start)

%F E.g.f.: exp(2*x)*(exp(4*x) - exp(3*x) - exp(2*x) - exp(x) + 4)/2.

%F a(n) = 20*a(n-1) - 155*a(n-2) + 580*a(n-3) - 1044*a(n-4) + 720*a(n-5) for n > 4. (End)

%t LinearRecurrence[{20,-155,580,-1044,720},{1,1,1,16,199},40] (* _Harvey P. Dale_, Jan 20 2022 *)

%Y Cf. A081680.

%K easy,nonn

%O 0,4

%A _Paul Barry_, Mar 30 2003