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

Offset: 1

Author

Anthony Labarre, Dec 25 2010

Keywords

• nonn

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).

Examples

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

Links

• 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.

Programs

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

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.)

Extensions

More terms from Michel Marcus, Oct 14 2024