|
|
A178217
|
|
Number of unsigned permutations in S_{3n-1} whose breakpoint graph contains only cycles of length 3.
|
|
0
|
|
|
1, 12, 464, 38720, 5678400, 1294720000, 423809075200, 188422340198400, 109244157102080000, 80068011114291200000, 72384558633074688000000, 79125533869852634644480000
(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
|
|
|
FORMULA
|
a(n) = (3n)!/(n!*12^n)*Sum_{i=0..n} binomial(n,i)*3^i)/(2i+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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|