A000183 -id:A000183 - cp's OEIS frontend

A002634 From discordant permutations.

-2, 3, 0, 25, 152, 1350, 12644, 131391, 1489568, 18329481, 243365514, 3468969962, 52848096274, 857073295427, 14744289690560, 268202790690465, 5143861702523924, 103746422699053582, 2195275169113687656, 48629604864202585247

Offset: 3

N. J. A. Sloane

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N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

K. Yamamoto, Structure polynomial of Latin rectangles and its application to a combinatorial problem, Memoirs of the Faculty of Science, Kyusyu University, Series A, 10 (1956), 1-13, DOI: 10.2206/kyushumfs.10.1
K. Yamamoto, Structure polynomial of Latin rectangles and its application to a combinatorial problem, Memoirs of the Faculty of Science, Kyusyu University, Series A, 10 (1956), 1-13. [Annotated scanned copy]

Cf. A000183.

a(n) = b(n) - 2*b(n-1) + b(n-2) + 2*a(n-1) + 2*a(n-2) - 2*a(n-3) + a(n-4) + 4*(-1)^n where b(n) = A000183(n) and n>6. a(3)=-2, a(4)=3, a(5)=0, a(6)=25. - Sean A. Irvine, May 03 2014

More terms from Sean A. Irvine, May 03 2014

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.

Original entry on oeis.org

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

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

The n-th row sums to n!.

			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;

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

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)

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

cp's OEIS Frontend

A002634 From discordant permutations.

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