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%I #2 Mar 30 2012 18:37:22
%S 1,2,38,352,8372,115584,4900168,109607936,5462020742,210689453568,
%T 11579697409448,585804318154752,39828186864515408,2482740302750253056,
%U 188760627291893696552,14430243196023615258624
%N a(n) = Sum_{k=0..n} C(n,k)*sigma(n,k)*sigma(n,n-k) for n>0 with a(0)=1.
%C sigma(n,k) denotes the sum of the k-th power of the divisors of n.
%e a(2) = 1*2*5 + 2*3*3 + 1*5*2.
%e a(3) = 1*2*28 + 3*4*10 + 3*10*4 + 1*28*2.
%e a(4) = 1*3*273 + 4*7*73 + 6*21*21 + 4*73*7 + 1*273*3.
%e a(5) = 1*2*3126 + 5*6*626 + 10*26*126 + 10*126*26 + 5*626*6 + 1*3126*2.
%e a(6) = 1*4*47450 + 6*12*8052 + 15*50*1394 + 20*252*252 + 15*1394*50 + 6*8052*12 + 1*47450*4.
%o (PARI) a(n)=if(n==0,1,sum(k=0,n,binomial(n,k)*sigma(n,k)*sigma(n,n-k)))
%K nonn
%O 0,2
%A _Paul D. Hanna_, Sep 21 2010