A178217 - OEIS

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A178217

Number of unsigned permutations in S_{3n-1} whose breakpoint graph contains only cycles of length 3.

1, 12, 464, 38720, 5678400, 1294720000, 423809075200, 188422340198400, 109244157102080000, 80068011114291200000, 72384558633074688000000, 79125533869852634644480000, 102879028406438808699535360000, 156917389218035568246207283200000, 277479100225377558605912342528000000

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

The number of permutations in S_{n} whose breakpoint graph contains only cycles of length 3 is nonzero only for n=3*k-1 (see references for definitions).

LINKS

Table of n, a(n) for n=1..15.

J.-P. Doignon and A. Labarre, On Hultman Numbers, J. Integer Seq., 10 (2007), 13 pages.

A. Labarre, Combinatorial aspects of genome rearrangements and haplotype networks (2008), Ph. D. thesis.

FORMULA

a(n) = (3*n)!/(n!*12^n)*Sum_{i=0..n} binomial(n,i)*3^i/(2*i+1). (See references for a proof.)

EXAMPLE

See references for examples (nongraphical explanations do not help much).

PROG

(Maxima) a(p) := ((3*p)!/(p!*12^p))*sum(binomial(p, i)*(3^i)/(2*i+1), i, 0, p);

(PARI) a(n) = (3*n)!/(n!*12^n) * sum(i = 0, n, binomial(n, i)*3^i/(2*i+1)); \\ Michel Marcus, Sep 05 2013

CROSSREFS