A178217 - OEIS

%I #45 Oct 14 2024 01:31:09

%S 1,12,464,38720,5678400,1294720000,423809075200,188422340198400,

%T 109244157102080000,80068011114291200000,72384558633074688000000,

%U 79125533869852634644480000,102879028406438808699535360000,156917389218035568246207283200000,277479100225377558605912342528000000

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

%C 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).

%H J.-P. Doignon and A. Labarre, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL10/Doignon/doignon77.html">On Hultman Numbers</a>, J. Integer Seq., 10 (2007), 13 pages.

%H A. Labarre, <a href="http://difusion.ulb.ac.be/vufind/Record/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210470/Holdings">Combinatorial aspects of genome rearrangements and haplotype networks</a> (2008), Ph. D. thesis.

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

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

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

%o (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

%K nonn

%O 1,2

%A _Anthony Labarre_, Dec 25 2010

%E More terms from _Michel Marcus_, Oct 14 2024