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 A281881 Triangle read by rows: T(n,k) (n>=1, 2<=k<=n+1) is the number of k-sequences of balls colored with at most n colors such that exactly one ball is of a color seen previously in the sequence. 3
 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 (list; table; graph; refs; listen; history; text; internal format)
 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 Columns of table:   T(n,2) = A000027(n)   T(n,3) = A028896(n) Other sequences in table:   T(n,n+1) = A001286(n)   T(n,n) = A001804(n), n>=2 Sequence in context: A276817 A050125 A178667 * A206493 A304085 A302783 Adjacent sequences:  A281878 A281879 A281880 * A281882 A281883 A281884 KEYWORD nonn,tabl AUTHOR Jeremy Dover, Feb 01 2017 STATUS approved

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Last modified January 19 22:12 EST 2022. Contains 350466 sequences. (Running on oeis4.)