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%I #8 Apr 19 2024 18:05:03
%S 0,0,0,1,9,69,510,3740,27454,202321,1498074,11145324,83291428,
%T 625022772,4707757080,35579447280,269718129308,2050317850201,
%U 15625047614946,119347362039788,913501931766460,7005437509949364,53817428069374328,414107216180618608
%N Sequence of constants appearing in formula for expected number of inversions after a sequence of random adjacent transpositions.
%D H. Eriksson, K. Ericcson and J. Sjostrand, Expected inversion number after k adjacent transpositions, in Formal Power Series and Algebraic Combinatorics, ed. D. Krob et al., Springer, 2000, pp. 677-685.
%H N. Eriksen, <a href="http://www.math.kth.se/~niklas/publ/exp_inv_FPSAC.pdf">Expected number of inversions after a sequence of random adjacent transpositions - an exact expression</a>, Discr. Math., 298 (2005), 155-168.
%F See Maple code for formula (found by N. Eriksen).
%p A081616 := proc(n) local b, s,l; b := binomial; (1/2)*add( b(n-1, s-1)*(-1)^(s-1)*4^(n-s)*b(2*floor(s/2),floor(s/2))* add( l*b(2*ceil(s/2)-1, ceil(s/2)+l ), l=0..floor((s-1)/2) ), s=3..n); end;
%K nonn
%O 0,5
%A _N. J. A. Sloane_, Apr 23 2003