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%I #4 Mar 31 2012 13:20:25
%S 1,9,94,3625,18631,1120581,34793764,5692787001,29669041771,
%T 30708223774261,134127439064434,302304605103335861,
%U 2387352152511746837,109134149200789179825,24217460586461892638584
%N Numerator of 1^n/n + 2^n/(n-1) + 3^n/(n-2) +...+ (n-1)^n/2 + n^n/1.
%C a(p-1) is divisible by p^3 for prime p>3. a(p^2-1) is divisible by p^6 for prime p>3. a(p^3-1) is divisible by p^9 for prime p>3.
%F a(n) = numerator[ Sum[ i^n/(n+1-i), {i,1,n}].
%e a(1) = numerator[1/1] = 1
%e a(2) = numerator[1/2 + 4/1] = 9
%e a(3) = numerator[1/3 + 4/2 + 9/1] = 94
%e a(4) = numerator[1/4 + 4/3 + 9/2 + 16/1] = 3625
%t Table[Numerator[Sum[i^n/(n+1-i),{i,1,n}]],{n,1,20}]
%Y Cf. A001008, A027612.
%K frac,nonn
%O 1,2
%A _Alexander Adamchuk_, Jun 17 2006
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