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A292930 Triangle read by rows: T(n,k) (n>=1, 3<=k<=n+2) is the number of k-sequences of balls colored with at most n colors such that exactly three balls are the same color as some other ball in the sequence 1

%I

%S 1,2,8,3,24,60,4,48,240,480,5,80,600,2400,4200,6,120,1200,7200,25200,

%T 40320,7,168,2100,16800,88200,282240,423360,8,224,3360,33600,235200,

%U 1128960,3386880,4838400,9,288,5040,60480,529200,3386880,15240960,43545600,59875200,10,360,7200,100800,1058400,8467200,50803200,217728000,598752000,798336000

%N Triangle read by rows: T(n,k) (n>=1, 3<=k<=n+2) is the number of k-sequences of balls colored with at most n colors such that exactly three balls are the same color as some other ball in the sequence

%C Note that the three matching balls are necessarily the same color.

%F T(n, k) = binomial(k,3)*n!/(n+2-k)!.

%e n=1 => AAA -> T(1,3)=1;

%e n=2 => AAA,BBB -> T(2,3)=2;

%e AAAB,AABA,ABAA,BAAA,BBBA,BBAB,BABB,ABBB -> T(2,4)=8.

%e Triangle begins:

%e 1;

%e 2, 8;

%e 3, 24, 60;

%e 4, 48, 240, 480;

%e 5, 80, 600, 2400, 4200;

%e ...

%o (PARI) T(n, k) = binomial(k,3)*n!/(n+2-k)!;

%o tabl(nn) = for (n=1, nn, for (k=3, n+2, print1(T(n,k), ", ")); print()); \\ _Michel Marcus_, Sep 29 2017

%Y Columns of table: T(n,3) = A000027(n), T(n,4) = A033996(n).

%Y Other sequences in table: T(n,n+2) = A005990(n+1).

%K nonn,tabl

%O 1,2

%A _Jeremy Dover_, Sep 26 2017

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Last modified February 26 18:29 EST 2020. Contains 332293 sequences. (Running on oeis4.)