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A177262
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Triangle read by rows: T(n,k) is the number of permutations of {1,2,...,n} starting with exactly k consecutive integers (1<=k<=n).
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0
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1, 1, 1, 4, 1, 1, 18, 4, 1, 1, 96, 18, 4, 1, 1, 600, 96, 18, 4, 1, 1, 4320, 600, 96, 18, 4, 1, 1, 35280, 4320, 600, 96, 18, 4, 1, 1, 322560, 35280, 4320, 600, 96, 18, 4, 1, 1, 3265920, 322560, 35280, 4320, 600, 96, 18, 4, 1, 1, 36288000, 3265920, 322560, 35280, 4320
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OFFSET
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1,4
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COMMENTS
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Sum of entries in row n is n!.
Sum(k*T(n,k), k=1..n)=1!+2!+...+n!=A007489(n).
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LINKS
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FORMULA
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T(n,k)=(n-k)!(n-k) if k<n; T(n,n)=1.
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EXAMPLE
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T(4,2)=4 because we have 1243, 2314, 3412, and 3421.
Triangle starts:
1;
1,1;
4,1,1;
18,4,1,1;
96,18,4,1,1;
600,96,18,4,1,1
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MAPLE
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T := proc (n, k) if k = n then 1 elif k < n then factorial(n-k)*(n-k) else 0 end if end proc: for n to 11 do seq(T(n, k), k = 1 .. n) end do; # yields sequence in triangular form
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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