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A081616 Sequence of constants appearing in formula for expected number of inversions after a sequence of random adjacent transpositions. 1
0, 0, 0, 1, 9, 69, 510, 3740, 27454, 202321, 1498074, 11145324, 83291428, 625022772, 4707757080, 35579447280, 269718129308, 2050317850201, 15625047614946, 119347362039788, 913501931766460, 7005437509949364, 53817428069374328, 414107216180618608 (list; graph; refs; listen; history; text; internal format)
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: A125372 A165147 A075045 * A299915 A287818 A297222

Adjacent sequences:  A081613 A081614 A081615 * A081617 A081618 A081619

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Apr 23 2003

STATUS

approved

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Last modified December 3 16:20 EST 2020. Contains 338906 sequences. (Running on oeis4.)