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A281881
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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.
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3
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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
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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FORMULA
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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)!
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EXAMPLE
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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
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MATHEMATICA
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Table[Binomial[k, 2] n!/(n + 1 - k)!, {n, 8}, {k, 2, n + 1}] // Flatten (* Michael De Vlieger, Feb 02 2017 *)
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CROSSREFS
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Columns of table:
Other sequences in table:
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KEYWORD
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AUTHOR
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STATUS
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approved
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