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A281944 Triangle read by rows: T(n,k) (n>=1, 3<=k<=n+2) is the number of k-sequences of balls colored with n colors such that exactly two balls are of a color seen previously in the sequence. 2
1, 2, 14, 3, 42, 150, 4, 84, 600, 1560, 5, 140, 1500, 7800, 16800, 6, 210, 3000, 23400, 100800, 191520, 7, 294, 5250, 54600, 352800, 1340640, 2328480, 8, 392, 8400, 109200, 940800, 5362560, 18627840, 30240000, 9, 504, 12600, 196560, 2116800, 16087680, 83825280, 272160000, 419126400, 10, 630, 18000, 327600, 4233600, 40219200, 279417600, 1360800000, 4191264000, 6187104000 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
T(n, k) = (binomial(k,3) + 3*binomial(k,4)) * n! / (n+2-k)!.
T(n, k) = n*T(n-1,k-1) + (k-2)*A281881(n,k-1).
EXAMPLE
n=1 => AAA -> T(1,3)=1
n=2 => AAA,BBB -> T(2,3)=2
AAAB,AABA,ABAA,BAAA,BBBA,BBAB,BABB,ABBB,AABB,ABAB,ABBA,BAAB,BABA,BBAA -> T(2,4)=14
Triangle starts:
1
2, 14
3, 42, 150
4, 84, 600, 1560
5, 140, 1500, 7800, 16800
6, 210, 3000, 23400, 100800, 191520
7, 294, 5250, 54600, 352800, 1340640, 2328480
8, 392, 8400, 109200, 940800, 5362560, 18627840, 30240000
9, 504, 12600, 196560, 2116800, 16087680, 83825280, 272160000, 419126400
MATHEMATICA
Table[(Binomial[k, 3] + 3 Binomial[k, 4]) n!/(n + 2 - k)!, {n, 12}, {k, 3, n + 2}] // Flatten (* Michael De Vlieger, Feb 05 2017 *)
PROG
(PARI) T(n, k) = (binomial(k, 3) + 3*binomial(k, 4)) * n! / (n+2-k)!;
tabl(nn) = for (n=1, nn, for (k=3, n+2, print1(T(n, k), ", ")); print()); \\ Michel Marcus, Feb 04 2017
CROSSREFS
Columns of table: T(n,3) = A000027(n), T(n,4) = A163756(n).
Other sequences in table: T(n,n+2) = A037960(n).
Sequence in context: A138907 A336837 A276189 * A306724 A316909 A103979
KEYWORD
nonn,tabl
AUTHOR
Jeremy Dover, Feb 02 2017
STATUS
approved

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Last modified April 22 05:00 EDT 2024. Contains 371887 sequences. (Running on oeis4.)