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%I #4 Nov 07 2014 23:02:40
%S 1,3,2,18,6,114,24,792,120,6120,720,52560,5040,498960,40320,5201280,
%T 362880,59149440,3628800,729388800,39916800,9699782400,479001600,
%U 138431462400,6227020800,2110960051200,87178291200,34261068441600,1307674368000,589761139968000,20922789888000
%N Sequence of distinct least positive numbers such that the average of the first n terms is a factorial.
%F a(2*n-1) = n!.
%F a(2*n) = n!*(2*n^2+1).
%o (PARI) v=[]; n=0; while(n<10^7, num=(vecsum(v)+n); if(num%(#v+1)==0&&vecsearch(vecsort(v), n)==0, for(i=0, n, if(i!>(num/(#v+1)), break); if(i!==(num/(#v+1)), print1(n, ", "); v=concat(v, n); n=0; break))); n++)
%K nonn
%O 1,2
%A _Derek Orr_, Nov 05 2014