A002633 Related to discordant permutations. (Formerly M2384 N0946)

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

0,2

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

Table of n, a(n) for n=0..23.

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]

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)

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 *)

Crossrefs

Cf. A213170, A269953.

Sequence in context: A199668 A318377 A186203 * A070554 A076842 A077862

Adjacent sequences: A002630 A002631 A002632 * A002634 A002635 A002636

Keyword

sign,easy

Author

N. J. A. Sloane

Extensions

More terms from Wouter Meeussen

Status

approved