login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A056151 Distribution of maximum inversion table entry. 4
1, 1, 1, 1, 3, 2, 1, 7, 10, 6, 1, 15, 38, 42, 24, 1, 31, 130, 222, 216, 120, 1, 63, 422, 1050, 1464, 1320, 720, 1, 127, 1330, 4686, 8856, 10920, 9360, 5040, 1, 255, 4118, 20202, 50424, 80520, 91440, 75600, 40320, 1, 511, 12610, 85182, 276696, 558120, 795600, 851760, 685440, 362880 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

T(n,k) = number of permutations p of [n] such that max(p(i)-i)=k. Example: T(3,0)=1 because for p=123 we have max(p(i)-i)=0; T(3,1)=3 because for p=132, 213, 231 we have max(p(i)-i) =1; T(3,2)=2 because for p=312, 321 we have max(p(i)-i)=2. - Emeric Deutsch, Nov 12 2004

REFERENCES

E. Deutsch and I. M. Gessel, Problem 10634, Amer. Math. Monthly, 107 (2000), 567-568.

R. Sedgewick and Ph. Flajolet, "An Introduction to the Analysis of Algorithms", Addison-Wesley, 1996, ISBN 0-201-40009-X, table 6.10 (page 356)

LINKS

Alois P. Heinz, Rows n = 1..141, flattened

FORMULA

Table[ -((-1 + k)^(1 - k + n)*(-1 + k)!) + k^(-k + n)*k!, {n, 1, 9}, {k, 1, n} ]

T(n, k)=k!(k+1)^(n-k) - (k-1)!k^(n-k+1) if 0<k<=n; T(n, 0)=1. - Emeric Deutsch, Nov 12 2004

EXAMPLE

{1}, {1, 1}, {1, 3, 2}, {1, 7, 10, 6},

MAPLE

T:=proc(n, k) if k>0 and k<=n then k!*(k+1)^(n-k)-(k-1)!*k^(n-k+1) elif k=0 then 1 else 0 fi end: TT:=(n, k)->T(n, k-1): matrix(10, 10, TT);

CROSSREFS

Columns and diagonals give A000225, A056182, A000142, A056197.

Sequence in context: A192020 A171128 A122832 * A134436 A186370 A163626

Adjacent sequences:  A056148 A056149 A056150 * A056152 A056153 A056154

KEYWORD

nonn,tabl,easy

AUTHOR

Wouter Meeussen, Aug 05 2000

EXTENSIONS

More terms from Larry Reeves (larryr(AT)acm.org), Oct 03 2000

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified March 23 21:31 EDT 2017. Contains 283985 sequences.