%I #2 Mar 31 2012 13:20:27
%S 1,33,262,10325,7227,923027,4588732,49631229,29087285,1618749187,
%T 152762993,69307256941,191848206263,702044812445,9181629908344,
%U 2873944084323677,1547933530301469,1198197057199579439
%N Numerator of Sum[ i^3/(n-i+1)^2, {i,1,n}].
%C Prime p divides a(2p-1). Prime p divides a(3p-1), p>2. Prime p divides a(p-1), p>2. p^2 divides a(p^2-1) for prime p>2. p^3 divides a(p^3-1) for prime p>2. p^4 divides a(p^4-1) for prime p>2. p^5 divides a(p^5-1) for prime p>2.
%F a(n) = numerator[ Sum[i^3/(n-i+1)^2, {i,1,n}]].
%t Numerator[Table[Sum[i^3/(n-i+1)^2,{i,1,n}],{n,1,50}]]
%Y Cf. A007406, A001008, A027612.
%K frac,nonn
%O 1,2
%A _Alexander Adamchuk_, Jun 25 2006