OFFSET
1,3
COMMENTS
A permutation (alpha,beta) from S_n X S_n acts on pairs (p,q) producing (alpha(p), beta(q)) yielding a permutation of the pairs which is factored into cycles to produce the number of cycles. Compare to Stirling numbers of the first kind, which compute the same statistic for Z(S_n).
REFERENCES
F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, 1973, page 95, section 4.3.
LINKS
EXAMPLE
1
0, 3, 0, 1
0, 12, 8, 0, 9, 6, 0, 0, 1
0, 96, 0, 204, 0, 160, 0, 67, 0, 36, 0, 12, 0, 0, 0, 1
MAPLE
seq(CF(q), q=1..7); # CF is defined in the attached Maple file.
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Marko Riedel, Dec 13 2016
STATUS
approved