%I A072949
%S A072949 0,0,0,4,24,148,744,3696,17640,83420,390144,1817652,8438664,39117852,
%T A072949 181136304,838372452,3879505944
%N A072949 Number of permutations p of (1,2,3,...,n) such that sum(k=1,n,abs(k-p(k)))=2n.
%C A072949 Is a(n) always even?
%C A072949 More generally, T(n,k) (from A062869) appears to be even whenever k >
               = n. - Franklin T. Adams-Watters, Dec 11 2006. Max Alekseyev reports 
               that both conjectures are true.
%p A072949 with(linalg): f := (i,j) -> x^(abs(i-j)):for n from 1 to 17 do A := matrix(n,
               n,f): printf("%d,",coeff(permanent(A),x,2*n)) od: - Herman Jamke 
               (hermanjamke(AT)fastmail.fm), Apr 27 2008
%o A072949 (PARI) a(n)=sum(k=1,n!,if(sum(i=1,n,abs(i-component(numtoperm(n,k),i)))-2*n,
               0,1))
%Y A072949 Cf. A072948, A062869.
%Y A072949 Sequence in context: A045915 A052609 A077613 this_sequence A104531 A045738 
               A003288
%Y A072949 Adjacent sequences: A072946 A072947 A072948 this_sequence A072950 A072951 
               A072952
%K A072949 more,nonn
%O A072949 1,4
%A A072949 Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 20 2002
%E A072949 More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 27 2008