This site is supported by donations to The OEIS Foundation.

The OEIS is looking to hire part-time people to help edit core sequences, upload scanned documents, process citations, fix broken links, etc. - Neil Sloane, njasloane@gmail.com

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A279514 Number of terms in the cycle index Z(S_n X S_n) of the cartesian product of the symmetric group S_n with itself that contain q cycles, where 1 <= q <= n*n. (Triangular array.) 1
 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, 0, 2400, 1680, 480, 1824, 1200, 1300, 2300, 1600, 100, 400, 400, 225, 300, 70, 0, 100, 0, 0, 20, 0, 0, 0, 0, 1, 0, 34560, 0, 87840, 0, 153840, 0, 77616, 0, 61020, 0, 56048, 0, 28500, 0, 9900, 0, 4075, 0, 3225, 0, 1350, 0, 170, 0, 225, 0, 0, 0, 30, 0, 0, 0, 0, 0, 1, 0, 2540160, 2338560, 1058400, 1522080, 1582560, 1225440, 1905120, 3605616, 2342592, 1605240 (list; graph; refs; listen; history; text; internal format)
 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 Marko R. Riedel, Maple code for cycle index and cycle count. 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 Sequence in context: A210473 A185951 A188832 * A094675 A200472 A263753 Adjacent sequences:  A279511 A279512 A279513 * A279515 A279516 A279517 KEYWORD nonn,tabf AUTHOR Marko Riedel, Dec 13 2016 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 27 22:57 EDT 2017. Contains 287210 sequences.