OFFSET
1,2
COMMENTS
Number of k-sequences of balls colored with at most n colors such that exactly two balls are the same color as some other ball in the sequence (necessarily each other, Jeremy Dover, Sep 26 2017
LINKS
Jeremy Dover, Table of n, a(n) for n = 1..999
FORMULA
T(n,k) = binomial(k,2)*n!/(n+1-k)!
T(n,k) = n*T(n-1,k-1) + (k-1)*n!/(n+1-k)!
EXAMPLE
n=1 => AA -> T(1,2) = 1.
n=2 => AA, BB -> T(2,2) = 2; AAB, ABA, BAA, BBA, BAB, ABB -> T(2,3) = 6.
Triangle starts:
1
2, 6
3, 18, 36
4, 36, 144, 240
5, 60, 360, 1200, 1800
6, 90, 720, 3600, 10800, 15120
7, 126, 1260, 8400, 37800, 105840, 141120
8, 168, 2016, 16800, 100800, 423360, 1128960, 1451520
9, 216, 3024, 30240, 226800, 1270080, 5080320, 13063680, 16329600
10, 270, 4320, 50400, 453600, 3175200, 16934400, 65318400, 163296000, 199584000
MATHEMATICA
Table[Binomial[k, 2] n!/(n + 1 - k)!, {n, 8}, {k, 2, n + 1}] // Flatten (* Michael De Vlieger, Feb 02 2017 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Jeremy Dover, Feb 01 2017
STATUS
approved