A081616 Sequence of constants appearing in formula for expected number of inversions after a sequence of random adjacent transpositions.

0, 0, 0, 1, 9, 69, 510, 3740, 27454, 202321, 1498074, 11145324, 83291428, 625022772, 4707757080, 35579447280, 269718129308, 2050317850201, 15625047614946, 119347362039788, 913501931766460, 7005437509949364, 53817428069374328, 414107216180618608

Offset

0,5

References

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.

Links

Table of n, a(n) for n=0..23.

N. Eriksen, Expected number of inversions after a sequence of random adjacent transpositions - an exact expression, Discr. Math., 298 (2005), 155-168.

Formula

See Maple code for formula (found by N. Eriksen).

Maple

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;

Crossrefs

Sequence in context: A165147 A075045 A361139 * A299915 A287818 A297222

Adjacent sequences: A081613 A081614 A081615 * A081617 A081618 A081619

Keyword

nonn

Author

N. J. A. Sloane, Apr 23 2003

Status

approved