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%I #2 Mar 31 2012 13:20:26
%S 0,4,27,428,1375,15797,211631,86540,1496205,144045379,145607407,
%T 3378951221,17021747431,51392118293,214084856611,13337033800292,
%U 13393340889767,94103945740529,3493457389196573,3503912518228613
%N Difference between numerator and denominator of the sum of all matrix elements of n X n Hilbert matrix M(i,j)=1/(i+j-1) (i,j = 1..n), A117731[n] - A117664[n].
%C p^3 divides a(p^k) for prime p>2 and integer k>0.
%F a(n) = Numerator[Sum[Sum[1/(i+j-1),{i,1,n}],{j,1,n}]] - Denominator[Sum[Sum[1/(i+j-1),{i,1,n}],{j,1,n}]]. a(n) = A117731[n] - A117664[n].
%t Numerator[Table[Sum[Sum[1/(i+j-1),{i,1,n}],{j,1,n}],{n,1,25}]] - Denominator[Table[Sum[Sum[1/(i+j-1),{i,1,n}],{j,1,n}],{n,1,25}]]
%Y Cf. A117731, A117664.
%K nonn
%O 1,2
%A _Alexander Adamchuk_, Jul 22 2006
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