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a(n) = 5^n - 4^n - 3^n - 2^n + 3.
1

%I #14 Sep 12 2024 19:30:00

%S 1,-1,-1,29,275,1829,10739,59429,318275,1670789,8656979,44454629,

%T 226827875,1151991749,5830280819,29429454629,148249811075,

%U 745630312709,3745590106259,18797445635429,94264432179875,472428649241669,2366562219717299,11850466059333029,59322887352366275,296896476647946629

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

%C Inverse binomial transform of A081685.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (15,-85,225,-274,120).

%F G.f.: (-1-254*x^4+266*x^3-99*x^2+16*x)/((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 From _Elmo R. Oliveira_, Sep 12 2024: (Start)

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

%F a(n) = 15*a(n-1) - 85*a(n-2) + 225*a(n-3) - 274*a(n-4) + 120*a(n-5) for n > 4. (End)

%t Table[5^n-4^n-3^n-2^n+3,{n,0,40}] (* _Harvey P. Dale_, Apr 01 2011 *)

%Y Cf. A081685.

%K easy,sign

%O 0,4

%A _Paul Barry_, Mar 30 2003

%E a(24)-a(25) from _Elmo R. Oliveira_, Sep 12 2024