OFFSET
1,2
COMMENTS
Note that the three matching balls are necessarily the same color.
FORMULA
T(n, k) = binomial(k,3)*n!/(n+2-k)!.
EXAMPLE
n=1 => AAA -> T(1,3)=1;
n=2 => AAA,BBB -> T(2,3)=2;
AAAB,AABA,ABAA,BAAA,BBBA,BBAB,BABB,ABBB -> T(2,4)=8.
Triangle begins:
1;
2, 8;
3, 24, 60;
4, 48, 240, 480;
5, 80, 600, 2400, 4200;
...
PROG
(PARI) T(n, k) = binomial(k, 3)*n!/(n+2-k)!;
tabl(nn) = for (n=1, nn, for (k=3, n+2, print1(T(n, k), ", ")); print()); \\ Michel Marcus, Sep 29 2017
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Jeremy Dover, Sep 26 2017
STATUS
approved