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%I #11 Oct 02 2013 15:12:32
%S 0,1,0,2,10,37,121,725,5160,31794,279136,2137531,21305316,213311303,
%T 2457648287,30357607661,387013387043,5245097770693
%N Number of permutations p of (1,2,3,...,n) such that sigma(1+p(1))+sigma(2+p(2))+...+sigma(n+p(n))=2*n^2.
%C It seems that for any permutation p of (1,2,3,...,n) for n>3, the equation: sigma(1+p(1))+sigma(2+p(2))+...+sigma(n+p(n))=m*n^2 has solutions for m=2 only.
%o (PARI) a(n)=sum(k=1,n!,if(sum(i=1,n, sigma(i+component(numtoperm(n,k),i)))-2*n^2,0,1))
%K nonn
%O 1,4
%A _Benoit Cloitre_, Aug 19 2002
%E 2 more terms from _Ryan Propper_, Aug 27 2005
%E a(12)-a(18) from _Robert Gerbicz_, Nov 21 2010
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