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a(n) = 7^n - 6^n - 5^n - 4^n + 3*3^n.
1

%I #16 Sep 12 2024 19:33:17

%S 1,1,-1,19,467,5611,53459,455659,3648707,28119691,211372019,

%T 1562038699,11405181347,82545287371,593501306579,4245828252139,

%U 30255066944387,214924122640651,1522971386761139,10770190567911979,76039651374633827,536127709619251531,3775797660906839699,26567026101757594219

%N a(n) = 7^n - 6^n - 5^n - 4^n + 3*3^n.

%C Binomial transform of A081685.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (25,-245,1175,-2754,2520).

%F G.f.: -(1326*x^4-886*x^3+219*x^2-24*x+1)/((3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)*(7*x-1)). [_Colin Barker_, Sep 07 2012]

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

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

%F a(n) = 25*a(n-1) - 245*a(n-2) + 1175*a(n-3) - 2754*a(n-4) + 2520*a(n-5) for n > 4. (End)

%Y Cf. A081685, A081687.

%K easy,sign

%O 0,4

%A _Paul Barry_, Mar 30 2003

%E a(22)-a(23) from _Elmo R. Oliveira_, Sep 12 2024