A094315 Triangle read by rows giving number of circular permutations of n letters such that all letters are displaced by no more than k places from their original position.

1, 0, 1, 0, 0, 2, 0, 0, 0, 6, 1, 0, 6, 8, 9, 2, 15, 20, 40, 30, 13, 20, 72, 180, 176, 180, 72, 20, 144, 609, 1106, 1421, 980, 595, 154, 31, 1265, 4960, 9292, 10352, 8326, 4096, 1676, 304, 49

Offset

0,6

Comments

The n-th row sums to n!.

References

J. Riordan, Discordant permutations, Scripta Math., 20 (1954), 14-23.

Links

Table of n, a(n) for n=0..44.

Anthony C. Robin, 90.72 Circular Wife Swapping, The Mathematical Gazette, Vol. 90, No. 519 (Nov., 2006), pp. 471-478.

J. Riordan, Discordant permutations, Scripta Math., 20 (1954), 14-23. [Annotated scanned copy] (See Table 2)

Formula

Riordan (1954) is devoted to the study of these numbers and gives generating functions (involving the numbers in A061702 as coefficients).

Example

1;
0, 1;
0, 0, 2;
0, 0, 0, 6;
1, 0, 6, 8, 9;
2, 15, 20, 40, 30, 13;
20, 72, 180, 176, 180, 72, 20;
144, 609, 1106, 1421, 980, 595, 154, 31;

Crossrefs

Diagonals give A000183 (which has further references), A000476, A000388, A000380, A000440, etc.

See also A061702.

Sequence in context: A053203 A158360 A309746 * A212148 A364988 A358622

Adjacent sequences: A094312 A094313 A094314 * A094316 A094317 A094318

Keyword

nonn,tabl

Author

N. J. A. Sloane, based on a suggestion from Anthony C Robin, Jun 02 2004

Status

approved