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A177262 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). 0
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,4
COMMENTS
Sum of entries in row n is n!.
T(n,1)=A094258(n)=(n-1)!(n-1).
Sum(k*T(n,k), k=1..n)=1!+2!+...+n!=A007489(n).
LINKS
FORMULA
T(n,k)=(n-k)!(n-k) if k<n; T(n,n)=1.
EXAMPLE
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
MAPLE
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
CROSSREFS
Sequence in context: A173814 A176467 A034802 * A203092 A139167 A211709
KEYWORD
nonn,tabl
AUTHOR
Emeric Deutsch, May 15 2010
STATUS
approved

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Last modified March 28 07:33 EDT 2024. Contains 371235 sequences. (Running on oeis4.)