A175771 - OEIS

%I #18 Sep 08 2022 08:45:51

%S 1,3,37,1305,95051,11878363,2277696793,622353150177,229930796172439,

%T 110462212541120451,66954547910007962117,49988751334503886046233,

%U 45082285083777592171142467,48321795074001873489007405947

%N a(n) = ((n^2 + 1)^n - 1)/n^3.

%C If we consider the general case ((n^(p-1) + 1)^n - 1)/n^p, we obtain this sequence for p=3, the sequence A060073 for p = 2, and the sequence A000051 for n = 2 and p = 2,3,...

%H Vincenzo Librandi, <a href="/A175771/b175771.txt">Table of n, a(n) for n = 1..200</a>

%e a(3) = ((3^2 + 1)^3 - 1)/3^3 = 999/27 = 37.

%p seq(((n^2 + 1)^n - 1)/n^3,n=1..10) ;

%t Table[((n^2 + 1)^n - 1)/n^3, {n,1,20}] (* _G. C. Greubel_, Nov 11 2018 *)

%o (Magma) [((n^2 + 1)^n - 1)/n^3 : n in [1..20]]; // _Vincenzo Librandi_, Sep 01 2011

%o (PARI) vector(20, n, ((n^2 + 1)^n - 1)/n^3) \\ _G. C. Greubel_, Nov 11 2018

%Y Cf. A060073, A000051.

%K nonn,easy

%O 1,2

%A _Michel Lagneau_, Sep 01 2010