A360961 Triangle T(m,n) read by rows: the number of homomorphisms of the complete graph on n vertices to the quasi-complete graph on m vertices, m>=3, 3<=n<m.

12, 42, 48, 96, 216, 240, 180, 600, 1320, 1440, 300, 1320, 4320, 9360, 10080, 462, 2520, 10920, 35280, 75600, 80640, 672, 4368, 23520, 100800, 322560, 685440, 725760, 936, 7056, 45360, 241920, 1028160, 3265920, 6894720, 7257600, 1260, 10800, 80640, 514080, 2721600, 11491200, 36288000, 76204800, 79833600

Offset

3,1

Links

Table of n, a(n) for n=3..47.

Pedro Lopes, Partial Profiles of Quasi-Complete Graphs, JIS vol 19 (2016) # 16.2.5 Propos. 1

Formula

T(m,n) = (m-1)!*2 if n=m-1, = n!*(binomial(m-2,n-1)*2+binomial(m-2,n)) if n<= m-2.

Example

The triangle starts
   12
   42    48
   96   216   240
  180   600  1320  1440
  300  1320  4320  9360 10080
  462  2520 10920 35280 75600 80640

Crossrefs

Sequence in context: A022672 A287152 A109275 * A241854 A085798 A335150

Adjacent sequences: A360958 A360959 A360960 * A360962 A360963 A360964

Keyword

nonn,tabl,easy

Author

R. J. Mathar, Feb 27 2023

Status

approved