|
|
A369923
|
|
Array read by antidiagonals: A(n,k) is the number of permutations of n copies of 1..k with values introduced in order and without cyclically adjacent elements equal.
|
|
7
|
|
|
0, 1, 0, 1, 1, 0, 1, 4, 1, 0, 1, 31, 22, 1, 0, 1, 293, 1415, 134, 1, 0, 1, 3326, 140343, 75843, 866, 1, 0, 1, 44189, 20167651, 83002866, 4446741, 5812, 1, 0, 1, 673471, 3980871156, 158861646466, 55279816356, 276154969, 40048, 1, 0
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,8
|
|
COMMENTS
|
Also, T(n,k) is the number of generalized chord labeled loopless diagrams with k parts of K_n. See the Krasko reference for a full definition.
|
|
LINKS
|
|
|
EXAMPLE
|
Array begins:
n\k| 1 2 3 4 5 6 ...
---+-----------------------------------------------------------
1 | 0 1 1 1 1 1 ...
2 | 0 1 4 31 293 3326 ...
3 | 0 1 22 1415 140343 20167651 ...
4 | 0 1 134 75843 83002866 158861646466 ...
5 | 0 1 866 4446741 55279816356 1450728060971387 ...
6 | 0 1 5812 276154969 39738077935264 14571371516350429940 ...
...
|
|
PROG
|
q(n, x) = sum(i=1, n, (-1)^(n-i) * binomial(n-1, n-i) * x^i/i!)
T(n, k) = if(k > 1, subst(serlaplace(n*q(n, x)^k/x), x, 1)/(k-1)!, 0)
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|