%I A062869
%S A062869 1,1,1,1,2,3,1,3,7,9,4,1,4,12,24,35,24,20,1,5,18,46,93,137,148,136,100,
%T A062869 36,1,6,25,76,187,366,591,744,884,832,716,360,252,1,7,33,115,327,765,
%U A062869 1523,2553,3696,4852,5708,5892,5452,4212,2844,1764,576,1,8,42,164,524
%N A062869 Triangle read by rows: For n >= 1, k >= 0, T(n,k) = the number of permutations 
               pi of n such that the total distance sum_i abs(i-pi(i)) = 2k. Equivalently, 
               k = sum_i max(i-pi(i),0).
%C A062869 Number of possible values is 1,2,3,5,7,10,13,17,21,... = A033638. Maximum 
               distance divided by 2 is the same minus one, i.e. 0,1,2,4,6,9,12,
               16,20,... = A002620.
%e A062869 1; 1,1; 1,2,3; 1,3,7,9,4; 1,4,12,24,35,24,20; ...
%e A062869 (4,3,1,2) has distances (3,1,2,2), sum is 8 and there are 4 other permutations 
               of degree 4 with this sum.
%Y A062869 Cf. A062866, A062867, A062870, A072949.
%Y A062869 Sequence in context: A059397 A152821 A071943 this_sequence A102473 A011117 
               A069269
%Y A062869 Adjacent sequences: A062866 A062867 A062868 this_sequence A062870 A062871 
               A062872
%K A062869 nonn,tabf
%O A062869 1,5
%A A062869 Olivier Gerard (olivier.gerard(AT)gmail.com), Jun 26 2001