OFFSET
1,3
COMMENTS
This is a special case (k=3) of a general (n,k)-team-hiring-problem, which is an extension to the assistant-hiring problem in Section 5.1 of the textbook Introduction to Algorithms by T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein.
LINKS
Jin-Yi Liu, On a problem of team hiring, hal-02485153, Computer Science [cs], 2020.
FORMULA
a(n) = n*a(n-1) + (n-1)*s(n-1,3) + (2n-1)*s(n-1,2) + (n-2)!, with the initial condition a(3)=6, and with s(n,k) being the unsigned Stirling number of the first kind.
PROG
(PARI) a(n) = if (n<=2, 0, if (n==3, 6, n*a(n-1) + (n-1)*abs(stirling(n-1, 3, 1)) + (2*n-1)*abs(stirling(n-1, 2, 1)) + (n-2)!)); \\ Michel Marcus, Jun 30 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Jin-Yi Liu, Jun 28 2019
EXTENSIONS
More terms from Michel Marcus, Jun 30 2019
STATUS
approved