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A173319 a(n) = 5*n! + 1.

%I A173319 #20 Dec 03 2024 19:53:15
%S A173319 6,6,11,31,121,601,3601,25201,201601,1814401,18144001,199584001,
%T A173319 2395008001,31135104001,435891456001,6538371840001,104613949440001,
%U A173319 1778437140480001,32011868528640001,608225502044160001,12164510040883200001,255454710858547200001
%N A173319 a(n) = 5*n! + 1.
%H A173319 Vincenzo Librandi, <a href="/A173319/b173319.txt">Table of n, a(n) for n = 0..200</a>
%F A173319 a(0)=6; for n>0, a(n) = n*a(n-1)-n+1. - _Vincenzo Librandi_, Sep 28 2013
%F A173319 (n-2)*a(n) - (n^2-n-1)*a(n-1) + (n-1)^2*a(n-2) = 0. [_Bruno Berselli_, Sep 28 2013]
%p A173319 A173319:=n->5*n!+1: seq(A173319(n), n=0..20); # _Wesley Ivan Hurt_, Oct 10 2014
%t A173319 Table[5 n! + 1, {n, 0, 20}] (* _Vincenzo Librandi_, Sep 28 2013 *)
%o A173319 (Magma) [5*Factorial(n) + 1: n in [0..20]]; // _Vincenzo Librandi_, Sep 28 2013
%o A173319 (Magma) [6] cat [n eq 1 select n+5 else n*Self(n-1)-n+1: n in [1..25] ]; // _Vincenzo Librandi_, Sep 28 2013
%Y A173319 Cf. sequences of the type k*n!+1: A038507 (k=1), A052898 (k=2), A173324 (k=3), A173322 (k=4), this sequence, A173314 (k=6).
%K A173319 nonn,easy
%O A173319 0,1
%A A173319 _Vincenzo Librandi_, Feb 16 2010