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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

Table of n, a(n) for n=1..60.

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

Cf. A094258, A007489

Sequence in context: A173814 A176467 A034802 * A203092 A139167 A211709

Adjacent sequences:  A177259 A177260 A177261 * A177263 A177264 A177265

KEYWORD

nonn,tabl

AUTHOR

Emeric Deutsch, May 15 2010

STATUS

approved

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Last modified November 28 01:24 EST 2021. Contains 349396 sequences. (Running on oeis4.)