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%I #8 Oct 22 2024 16:04:10
%S -1,-2,0,16,110,708,5026,40304,362862,3628780,39916778,479001576,
%T 6227020774,87178291172,1307674367970,20922789887968,355687428095966,
%U 6402373705727964,121645100408831962,2432902008176639960,51090942171709439958,1124000727777607679956,25852016738884976639954,620448401733239439359952
%N n!-2n.
%C For n > 2, a(n) is the largest value of k such that (n!+k)/(n+k) is an integer.
%C For n > 2, a(n) is the largest value of k such that (n!+k)/(n+k) is prime.
%C For n > 1, a(n) is even.
%F a(n) = n!-2n.
%e 3!-2*3 = 0 so a(3) = 0.
%e 4!-2*4 = 16 so a(4) = 16.
%e 5!-2*5 = 110 so a(5) = 110.
%t Table[n!-2n,{n,30}] (* _Harvey P. Dale_, Oct 22 2024 *)
%o (Python)
%o import math
%o {print(math.factorial(n)-2*n) for n in range(1,25)}
%o (PARI) for(n=1,25,print(n!-2*n))
%Y Cf. A000142, A242567, A242568.
%K sign
%O 1,2
%A _Derek Orr_, May 17 2014