A002633 Related to discordant permutations.

1, -3, 5, -3, 9, -3, -51, -675, -5871, -46467, -331371, -1852227, -920295, 224455293, 5571057501, 104877816093, 1781775072801, 28519837563645, 431525731169061, 5994769814117757, 68879336771960361, 346333945918252797, -15047168730918615315, -793523760950138583843

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign
• easy

References

• 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).

Links

• 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.
• 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]

Crossrefs

Cf. A213170, A269953.

Programs

Mathematica

a[ n_ ] := a[ n ]=(2n-5)a[ n-1 ]-(n-1)(n-4)a[ n-2 ]-(n-1)(n-2)a[ n-3 ]; a[ 0 ]=1; a[ 1 ]=-3; a[ 2 ]=5; Table[ a[ n ], {n, 0, 24} ] (* Typo fixed by Vaclav Kotesovec, Mar 20 2014 *)

Formula

a(n) - (2n-5)*a(n-1) + (n-1)*(n-4)*a(n-2) + (n-1)*(n-2)*a(n-3) = 0.

From Mélika Tebni, Mar 02 2022: (Start)

a(n) = Sum_{k=0..n} A213170(k)*A269953(n, k).

E.g.f.: exp(-x*(3 - x) / (1 - x)). (End)

Extensions

More terms from Wouter Meeussen