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%I #2 Mar 31 2012 13:21:57
%S 0,3,3,1,5,0,7,4,6,2,11,5,13,4,7,8,17,6,19,9,11,8,23,8,20,10,18,13,29,
%T 10,31,16,19,14,23,12,37,16,23,16,41,14,43,21,24,20,47,16,42,20,31,25,
%U 53,18,39,24,35,26,59,15,61,28,36,32,47,22,67,33,43,26,71,24,73,34,40
%N Derived from a(n)=binomial(n+1,2) - sum{i=1,n-1,a(i)*floor(n/i)} (see A000010) - this is the value of the constant term.
%C It is conjectured that a(n) is never less than 0 (tested to n=2000)
%e The formula produces the initial output:
%e x, -2*x + 3, -x + 3, x + 1, -x + 5, 2*x, -x + 7, 4, 6, 2*x + 2, -x + 11, -x + 5, -x + 13, 2*x + 4, x + 7, 8, -x + 17, 6, -x + 19, -x + 9, x + 11, 2*x + 8, -x + 23, 8, 20, 2*x + 10, 18, -x + 13, -x + 29, -2*x + 10, -x + 31, 16, x + 19.
%e The sequence gives the constant term.
%o (PARI) s=vector(200); t(n)=binomial(n+1,2); s[1]=x; for(i=2,200, s[i]=t(i)-sum(j=1,i-1, s[j]*floor(i/j))); for(i=1,200,print1(","polcoeff(s[i],0)))
%Y Cf. A092673.
%K nonn
%O 1,2
%A _Jon Perry_, Mar 02 2004