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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 Jeremy Dover, Table of n, a(n) for n = 1..1035 Jeremy Dover, Answer to Cumulative Distribution Function of Collision Counts 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 Adjacent sequences: A281941 A281942 A281943 * A281945 A281946 A281947 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.)