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
Andrew Howroyd, Table of n, a(n) for n = 1..1275 (first 51 antidiagonals)
Evgeniy Krasko, Igor Labutin, and Alexander Omelchenko, Enumeration of Labelled and Unlabelled Hamiltonian Cycles in Complete k-partite Graphs, arXiv:1709.03218 [math.CO], 2017.
Mathematics.StackExchange, Find the number of k 1's, k 2's, ... , k n's - total kn cards, Apr 08 2012.
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
(PARI) \\ compare with A322013.
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
nonn,tabl
AUTHOR
Andrew Howroyd, Feb 05 2024
STATUS
approved